the co printing problem a packing problem with a color constraint the co printing problem is a new variant of the bin packing problem it finds its origin in the printing of tetra bricks in the beverage industry combining different types of bricks in one printing pattern reduces the stock with each brick a number of colors are associated and the total number of colors for the whole pattern cannot exceed a given limit we develop a branch and price algorithm to obtain proven optimal solutions after introducing a dantzig wolfe reformulation for the problem we derive cutting planes to tighten the lp relaxation we present heuristics and develop a branching scheme avoiding complex pricing problem modifications we present some further algorithmic enhancements such as the implementation of dominance rules and a lower bound based on a combinatorial relaxation finally we discuss computational results for real life data sets in addition to the introduction of a new bin packing problem this paper illustrates the complex balance in branch and price algorithms among using cutting planes the branching scheme and the tractability of the pricing problem it also shows how dominance rules can be implemented in a branch and price framework resulting in a substantial reduction in computation time

homogenization of fully nonlinear uniformly elliptic and parabolic partial differential equations in stationary ergodic media we study the homogenization of fully nonlinear uniformly elliptic and parabolic second order partial differential equations in stationary ergodic media c 2004 wiley periodicals inc

weak type 1 1 inequalities and regularity properties of adjoint and normalized adjoint solutions to linear nondivergence form operators with vmo coefficients

boundary regularity on the parabolic monge ampere equation abstract this paper establishes boundary estimates for solutions to the parabolic monge ampere equation u t det d 2 u 1 n f x t

lagrange type extremal trajectories in differential inclusions abstract necessary conditions for optimal or boundary solutions of differential inclusions usually state that such solutions are extremal in some sense there are several possible concepts of extremality which lead to different often difficult to compare necessary conditions in this paper we give a complete comparison of three classes of extremal trajectories two different lagrange type extremals and hamiltonian extremals in the second part we consider a nonconvex differential inclusion and prove that every boundary trajectory is a lagrangian extremal

a control problem related to the parabolic dominative p laplace equation abstract we show that value functions of a certain time dependent control problem in 0 t with a continuous payoff f on the parabolic boundary converge uniformly to the viscosity solution of the parabolic dominative p laplace equation 2 n p u t u p 2 n d 2 u with the boundary data f here 2 p and n d 2 u is the largest eigenvalue of the hessian d 2 u

fujita type exponent for fully nonlinear parabolic equations and existence results abstract in this paper we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a fujita type exponent these exponents are related with an eigenvalue problem in all r n and play the same role in blow up theorems as the classical p 1 2 n introduced by fujita for the laplacian we also obtain some associated existence results

the regularity theory for the parabolic double obstacle problem in this paper we study the regularity of the free boundaries of the parabolic double obstacle problem for the heat operator and fully nonlinear operator the result in this paper are generalizations of the theory for the elliptic problem in lee et al calc var partial differ equ 58 3 104 2019 and lee and park the regularity theory for the double obstacle problem for fully nonlinear operator 2018 to parabolic case and also the theory for the parabolic single obstacle problem in caffarelli et al j am math soc 17 4 827 869 2004 to double obstacle case new difficulties in the theory which are generated by the characteristic of parabolic pdes and the existence of the upper obstacle are discussed in detail furthermore the thickness assumptions to have the regularity of the free boundary are carefully considered

a rate of convergence for monotone finite difference approximations to fully nonlinear uniformly elliptic pdes we obtain an algebraic rate of convergence for monotone and consistent finite difference approximations to lipschitz continuous viscosity solutions of uniformly elliptic partial differential equations 2007 wiley periodicals inc

maximum principle for fully nonlinear equations via the iterated comparison function method we present various versions of generalized aleksandrov bakelman pucci abp maximum principle for l p viscosity solutions of fully nonlinear second order elliptic and parabolic equations with possibly superlinear growth gradient terms and unbounded coefficients we derive the results via the iterated comparison function method which was introduced in our previous paper koike and wiech in nonlin diff eq appl 11 491 509 2004 for fully nonlinear elliptic equations our results extend those of koike and wiech in nonlin diff eq appl 11 491 509 2004 and fok in comm partial diff eq 23 5 6 967 983 in the elliptic case and of crandall et al in indiana univ math j 47 4 1293 1326 1998 comm partial diff eq 25 1997 2053 2000 wang in comm pure appl math 45 27 76 1992 and crandall and wiech in lecture notes in pure and applied mathematics vol 234 dekker new york 2003 in the parabolic case

aleksandrov bakelman pucci maximum principles for a class of uniformly elliptic and parabolic integro pde abstract we prove generalized aleksandrov bakelman pucci maximum principles for elliptic and parabolic integro pdes of hamilton jacobi bellman isaacs types whose pde parts are either uniformly elliptic or uniformly parabolic the proofs of these results are based on the classical aleksandrov bakelman pucci maximum principles for the elliptic and parabolic pdes and an iteration procedure using solutions of pucci extremal equations we also provide proofs of nonlocal versions of the classical aleksandrov bakelman pucci maximum principles for elliptic and parabolic integro pdes

perron s method for hamilton jacobi equations on considere l existence des solutions d equations aux derivees partielles non lineaires scalaires d ordre 1 f x u du 0 dans ou est un sous ensemble ouvert de r n f r r n r est continue u r est l inconnue

conjugate points for variational problems with equality and inequality state constraints in this paper variational problems with equality and inequality state constraints are considered the theory of conjugate points for these problems is developed and necessary conditions for weak local optimality are derived in terms of this concept and the legendre condition for the case of inequality constraints the envelope like effect is taken into consideration in the accessory problem

the adjoint arc in nonsmooth optimization we extend the theory of necessary conditions for nonsmooth problems of bolza in three ways first we incorporate state constraints of the intrinsic type x t e x t for all t second we make no assumption of calmness or normality and third we show that a single adjoint function of bounded variation simultaneously satisfies the hamiltonian inclusion the euler lagrange inclusion and the weierstrass pontryagin maximum condition along with the usual transversality relations

local regularity for quasi linear parabolic equations in non divergence form abstract we consider viscosity solutions to non homogeneous degenerate and singular parabolic equations of the p laplacian type and in non divergence form we provide local holder and lipschitz estimates for the solutions in the degenerate case we prove the holder regularity of the gradient our study is based on a combination of the method of alternatives and the improvement of flatness estimates

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

weak harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications abstract the weak harnack inequality for l p viscosity supersolutions of fully nonlinear second order uniformly parabolic partial differential equations with unbounded coefficients and inhomogeneous terms is proved it is shown that holder continuity of l p viscosity solutions is derived from the weak harnack inequality for l p viscosity supersolutions the local maximum principle for l p viscosity subsolutions and the harnack inequality for l p viscosity solutions are also obtained several further remarks are presented when equations have superlinear growth in the first space derivatives

on uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic pde s we prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations one of them extends some recent uniqueness results by jensen some establish the uniqueness of solutions for second order isaacs equations and hence include the uniqueness results for bellman equations by p l lions our comparison results apply even for discontinuous solutions and so perron s method readily yields the existence of continuous solutions

state constraints in optimal control the degeneracy phenomenon in this paper we study the degeneracy phenomenon arising in optimal control problems with state constraints it is shown that this phenomenon occurs because of the incompleteness of the standard variants of pontryagin s maximum principle for problems with state constraints the new maximum principle containing some additional information about the behavior of the hamiltonian at the endtimes is developed as application we obtain some sufficient and necessary conditions for nondegeneracy and pointwise nontriviality of the maximum principle the results obtained envelope the optimal control problems with systems described by differential inclusions and ordinary differential equations

elliptic equations on convex domains with nonhomogeneous dirichlet boundary conditions abstract in this paper we will study the differentiability on the boundary of solutions of elliptic non divergence differential equations on convex domains the results are divided into two cases i at the boundary points where the blow up of the domain is not the half space if the boundary function is differentiable then the solution is differentiable ii at the boundary points where the blow up of the domain is the half space the differentiability of the solution needs an extra dini condition for the boundary function counterexample is given to show that our results are optimal

necessary conditions for the neutral problem of bolza with continuously varying time delay this note uses clarke s decoupling technique to obtain necessary conditions for the generalized problem of bolza with lipschitz continuously varying delay in both the state and velocity variables

a column generation approach to job grouping for flexible manufacturing systems abstract a flexible manufacturing system consists of a number of nc machines linked by automated material handling devices that perform the various operations required to manufacture parts each operation requires different tools these tools are stored in a limited capacity tool magazine attached to each machine when it becomes necessary to add or remove tools from the tool magazine the machine may have to be shut down for a setup in this paper we study a model which aims at minimizing the number of setups we assume that n jobs must be processed on a machine each job requires a certain set of tools which have to be present in the tool magazine of the machine when the job is executed the magazine has a total capacity of c tools we say that a group subset batch of jobs is feasible if together these jobs do not require more than c tools the job grouping problem is to partition the jobs into a minimum number of feasible groups the problem can be formulated as a set covering problem we solve the linear relaxation of this formulation in order to obtain tight lower bounds since the number of variables is potentially huge we use a column generation approach the column generation subproblem turns out to be np hard we solve it by enumeration we also describe some fast and simple heuristics for the job grouping problem the result of our computational experiments is that the lower bound is extremely strong the quality of the heuristic solutions is in general very good too we also investigate a more general multiple machine model in which each tool may occupy several slots in the tool magazines

parabolic equations in time dependent reifenberg domains in this paper we define time dependent parabolic reifenberg domains and study lp estimates for weak solutions of uniformly parabolic equations in divergence form on these domains the basic assumption is that the principal coefficients are of parabolic bmo space with small parabolic bmo seminorms it is shown that lp estimates hold for time dependent parabolic d reifenberg domains

sharp regularity estimates for second order fully nonlinear parabolic equations we prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form begin aligned u t f left d 2u du x t right f x t quad text in quad q 1 end aligned eq where f is elliptic with respect to the hessian argument and f in l p q q 1 the quantity xi n p q frac n p frac 2 q determines to which regularity regime a solution of eq belongs we prove that when 1 xi n p q 2 epsilon f solutions are parabolically alpha holder continuous for a sharp quantitative exponent 0 alpha n p q 1 precisely at the critical borderline case xi n p q 1 we obtain sharp parabolic log lipschitz regularity estimates when 0 xi n p q 1 solutions are locally of class c 1 sigma frac 1 sigma 2 and in the limiting case xi n p q 0 we show parabolic c 1 text log lip regularity estimates provided f has better a priori estimates

auxiliary tool allocation in flexible manufacturing systems abstract this paper analyses a new approach to the machine loading problem arising in flexible manufacturing systems fmss this approach allows the operations to be assigned to machines assuming that machines have access to all the tools required for their operations this exploits the flexibility of the fms completely next an allocation of tools to machines is determined which satisfies the tool requirements for each machine and minimizes the total number of tools thus this approach minimizes the unnecessary tool duplications in the system and maximizes the tool utilization the problem is modeled as an integer linear program ilp we notice that the main problem has a block diagonal structure which is decomposable by relaxing a set of linking constraints each separated sub problem represents a problem of allocation of a single type of tools we develop a branch and bound based exact solution procedure and three heuristic procedures to solve the sub problems our lower bounding approach uses lanrangean relaxation the solutions to the lagrangean relaxation are further used to determine the branching sequences and to develop heuristic approaches since finding even a feasible solution to the main problem is np hard we develop only enumerative procedures to solve the main problem finally these solution procedures are tested on randomly generated test problems

holder gradient estimates for fully nonlinear elliptic equations in this paper we prove interior and global holder estimates for lipschitz viscosity solutions of second order nonlinear uniformly elliptic equations the smoothness hypotheses on the operators are more general than previously considered for classical solutions so that our estimates are also new in this case and readily extend to embrace obstacle problems in particular isaac s equations of stochastic differential game theory constitute a special case of our results and moreover our techniques in combination with recent existence theorems of ishii lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic isaac s equation

levy s martingale characterization and reflection principle of g brownian motion abstract in this paper by a new kind of discrete product space method for martingales we obtain levy s martingale characterization of g brownian motion without the nondegenerate condition based on this characterization we prove the reflection principle of g brownian motion furthermore we use krylov s estimate to get the reflection principle of the general g brownian motion

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

on the aleksandrov bakel man pucci estimate for some elliptic and parabolic nonlinear operators in this work we prove the aleksandrov bakel man pucci estimate for possibly degenerate nonlinear elliptic and parabolic equations of the form rm div left f left nabla u x right right f left x right quad rm in omega subset mathbb r n and u t x t rm div left f left nabla u x t right right f left x t right quad rm in q subset mathbb r n 1 for f a fancyscript c 1 monotone field under some suitable conditions examples of applications such as the p laplacian and the mean curvature flow are considered as well as extensions of the general results to equations that are not in divergence form such as the m curvature flow

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a connection between the maximum principle and dynamic programming for constrained control problems we consider the mayer optimal control problem with dynamics given by a nonconvex differential inclusion whose trajectories are constrained to a closed set and obtain necessary optimality conditions in the form of the maximum principle together with a relation between the costate and the value function this additional relation is applied in turn to show that the maximum principle is nondegenerate we also provide a sufficient condition for the normality of the maximum break principle to derive these results we use convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories then duality theory of convex analysis is applied to derive necessary conditions for optimality in this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case

weighted regularity estimates in orlicz spaces for fully nonlinear elliptic equations abstract in this paper we develop a global w 2 p estimate for the viscosity solution of the dirichlet problem of fully nonlinear elliptic equations f d 2 u d u u x f x in u 0 on to a more general function space given an n function and a muckenhoupt weight w we prove that if f belongs to the associated weighted orlicz space l w then d 2 u l w and u satisfies a global w w 2 estimate under a minimal regularity requirement on f in the variable x and a basic geometric assumption on the correct condition on the couple and w is also addressed this result generalizes the w 2 p estimate caffarelli 1989 escauriaza 1993 winter 2009 of calderon and zygmund as well as an analogous one byun et al 2016 in the weighted l p setting

higher order convergence rates in theory of homogenization ii oscillatory initial data abstract we establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic cauchy problems accompanied with rapidly oscillating initial data such result is new even for linear problems here we construct higher order initial layer and interior correctors which describe the oscillatory behavior near the initial and interior time zone of the domain to construct higher order correctors we develop a regularity theory in macroscopic scales and prove an exponential decay estimate for initial layer correctors the higher order expansion requires an iteration process successively correcting the initial layer then the interior this leads to a more complicated asymptotic expansion as compared to the non oscillating data case and this complexity is present even in the linear case a notable observation for fully nonlinear operators is that even if the given operator is space time periodic the interior correctors become aperiodic in the time variable as we proceed with the iteration process moreover each interior corrector of higher order is paired with a space time periodic version and the difference between the two decays exponentially fast with time

on a class of fully nonlinear flows in kahler geometry in this paper we study a class of fully nonlinear metric flow on kahler manifolds which includes the j flow as a special case we provide a sufficient and necessary condition for the long time convergence of the flow generalizing the result of songweinkove as a consequence under the given condition we solved the corresponding euler equation which is fully nonlinear of monge ampere type as an application we also discuss a complex monge ampere type equation including terms of mixed degrees which was first posed by chen

hamiltonian analysis of the generalized problem of bolza on obtient des conditions necessaires en forme hamiltonienne sous des hypotheses moins exigeantes qu anterieurement en particulier sans qualification sur les contraintes on developpe le lien avec les problemes de commande optimale ainsi que l apport de ces conditions a la theorie de la regularite de la solution

optimum problems with certain lower semicontinuous set valued constraints in this paper we provide a complete analysis of second order admissible variations to inequality type constraints that are given in terms of lower semicontinuous set valued functions whose images are closed convex sets with nonempty interior as an application we consider optimization problems where such constraints are present and we deduce second order necessary conditions for optimality

free boundary regularity close to initial state for parabolic obstacle problem here partial derivative p denotes the parabolic boundary h is a parabolic operator with certain properties q is the upper half of the unit cylinder in rn 1 and the equation is satisfied in t

explicit solutions of the g heat equation for a class of initial conditions abstract we obtain the viscosity solution of the g heat equation with the initial condition x x n for each integer n 1 using the method of g brownian motion

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

worn stones with flat sides all time regularity of the interface we study the all time regularity of the free boundary problem associated to the deformation of a compact weakly convex surface in 3 with a flat side by its gaussian curvature we show that under certain necessary regularity and non degeneracy initial conditions the interface separating the flat from the strictly convex side remains smooth on 0 t tc up to the vanishing time tc of the flat side

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

holder estimates in space time for viscosity solutions of hamilton jacobi equations it is well known that solutions to the basic problem in the calculus of variations may fail to be lipschitz continuous when the lagrangian depends on t similarly for viscosity solutions to time dependent hamilton jacobi equations one cannot expect lipschitz bounds to hold uniformly with respect to the regularity of coefficients this phenomenon raises the question whether such solutions satisfy uniform estimates in some weaker norm we will show that this is the case for a suitable holder norm obtaining uniform estimates in x t for solutions to first and second order hamilton jacobi equations our results apply to degenerate parabolic equations and require superlinear growth at infinity in the gradient variables of the hamiltonian proofs are based on comparison arguments and representation formulas for viscosity solutions as well as weak reverse holder inequalities 2010 wiley periodicals inc

dualization of the euler and hamiltonian inclusions optimal control emerged as a distinct eld of research in the late 1950s with the derivation of the pontryagin maximum principle a fundamental set of necessary conditions on minimizing arcs which takes account of di erential constraints the pontryagin maximum principle directly generates the euler equation and other classical necessary conditions from the calculus of variations when specialised to problems without dynamic constraints however deeper connections between necessary conditions in optimal control and the calculus of variations were only subsequently revealed when clarke developed new analytic machinery now referred to as nonsmooth analysis a term introduced by clarke himself for extending classical necessary conditions to apply to the generalized

solvability of uniformly elliptic fully nonlinear pde we get existence uniqueness and non uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the hamilton jacobi bellman isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness some of our results are new even for equations in divergence form

a remark on a vanishing property for viscosity solutions of fully nonlinear parabolic equations abstract we make the observation that under some natural conditions on f stated in a c in the main text if a viscosity solution of the fully nonlinear parabolic equation f d 2 u d u u u t 0 vanishes to infinite order at x 0 t 0 then there is a small spatial neighborhood b r 0 x 0 t 0 of x 0 t 0 in which u vanishes identically the proof is inspired in an essential way by the ideas employed in the recent paper armstrong and silvestre 2011 2 where the unique continuation property for fully nonlinear elliptic equations was established

holder estimates for non local parabolic equations with critical drift abstract in this paper we extend previous results on the regularity of solutions of integro differential parabolic equations the kernels are non necessarily symmetric which could be interpreted as a non local drift with the same order as the diffusion we provide a growth lemma and a harnack inequality which can be used to prove higher regularity estimates

the proximal normal formula in hilbert space on considere la formule normale proximale dans un espace de hilbert on presente une demonstration simple du theoreme de borwein strojwas

models arising from a flexible manufacturing machine part ii minimization of the number of switching instants this paper deals with a job scheduling problem for a flexible manufacturing machine we consider the same manufacturing environment described in a companion study part i but we use a different performance criterion to minimize the total number of instants at which tools are switched this performance criterion is appropriate when the switching time is roughly constant and independent of the number of tool switches we show that this scheduling problem generalizes the classical bin packing problem and we present a non lp based branch and bound procedure that terminates with an optimal solution we extend this procedure to the case of k machines in sequence

hypersurfaces with mean curvature given by an ambient sobolev function we consider n hypersurfaces j with interior ej whose mean curvature are given by the trace of an ambient sobolev function uj w 1 p r h j uj ej on j 0 1 where ej denotes the inner normal of j we investigate 0 1 when j weakly as varifolds and prove that is an integral n varifold with bounded first variation which still satisfies 0 1 for uj u ej e p has to satisfy

on the regularity theory of fully nonlinear parabolic equations ii recently m crandall and p l lions 3 developed a very successful method for proving the existence of solutions of nonlinear second order partial differential equations their method called the theory of viscosity solutions also applies to fully nonlinear equations in which even the second order derivatives can enter in nonlinear fashion solutions produced by the viscosity method are guaranteed to be continuous but not necessarily smooth here we announce smoothness results for viscosity solutions our methods extend those of 1 we obtain krylov safonov i e c estimates 8 c 1 schauder c and w estimates for viscosity solutions of uniformly parabolic equations in general form the results can be viewed as a priori estimates on the classical c solutions our method produces in particular regularity results for a broad new array of nonlinear heat equations including the bellman equation 6

regularity results on the parabolic monge ampere equation with vmo type data abstract this paper establishes interior estimates for l p norms orlicz norms of solutions to the parabolic monge ampere equation u t det d 2 u f x t provided that f x t is positive bounded and satisfies a vmo type condition and some integrability conditions for f t our results improve the corresponding results in gutierrez and huang 2001 8 in some sense

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

twice differentiability of solutions to fully nonlinear parabolic equations near the boundary abstract in this paper we prove h 2 regularity for viscosity solutions to non convex fully nonlinear parabolic equations near the boundary this constitutes the parabolic counterpart of a similar c 2 regularity result due to silvestre and sirakov proved in 17 for solutions to non convex fully nonlinear elliptic equations

on the occurrence of intermediate local minimizers that are not strong local minimizers abstract recently it has been shown by mordukhovich that certain necessary conditions of optimality in control theory are satisfied at intermediate local minimizers in addition to strong local minimizers it is of interest to know then whether the class of intermediate local minimizers differs from that of strong local minimizers we give examples illustrating that the two concepts of minimizers are indeed distinct and also distinguish intermediate minimizers of different rank we also extend the class of necessary conditions which are known to be satisfied at an intermediate local minimizer

hausdorff measure estimates and lipschitz regularity in inhomogeneous nonlinear free boundary problems in this paper we prove a hausdorff measure estimate for the free boundaries of subsolutions of fully nonlinear and quasilinear equations of the type f d 2u x geqq f x and rm div a x nabla u geqq mu where f in l q q n and is a signed radon measure with some appropriate growth condition gradient estimates for nonnegative harmonic functions with bounded normal derivatives along the boundary obtained by caffarelli and salsa geometric approach to free boundary problems 2005 are extended to the context of inhomogeneous problems involving fully nonlinear and p laplace equations as an application lipschitz regularity is obtained for one phase solutions of inhomogeneous nonlinear free boundary problems

on a prioric 1 α andw 2 p estimates for a parabolic monge ampere equation in the gauss curvature flows this paper establishes holder estimates of du and l p estimates of d 2 u for solutions u to the parabolic monge ampere equation au t det d 2 u 1 n

on the viscosity solutions of a stochastic differential utility problem we prove existence uniqueness and gradient estimates of stochastic differential utility as a solution of the cauchy problem for the following equation in r 3 xxu u yu tu f u where f is lipschitz continuous we also characterize the solution in the vanishing viscosity sense r 2002 elsevier science usa all rights reserved

nonlinear elliptic parabolic problems we introduce a notion of viscosity solutions for a general class of elliptic parabolic phase transition problems these include the richards equation which is a classical model in filtration theory existence and uniqueness results are proved via the comparison principle in particular we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data these results are new even in the linear case where we also show that viscosity solutions coincide with the regular weak solutions introduced in alt and luckhaus math z 183 311 341 1983

lateral boundary differentiability of solutions of parabolic equations in nondivergence form abstract the lateral boundary differentiability is shown for solutions of parabolic differential equations in nondivergence form under the assumptions that the parabolic boundary satisfies the exterior dini condition and is punctually c 1 differentiable one sided in t direction the classical barrier technique the maximum principle the interior harnack inequality and an iteration procedure are the main analytical tools

hamiltonian trajectories and duality in the optimal control of linear systems with convex costs a duality theorem is proved for problems of optimal control of linear dynamical systems in continuous time subject to linear constraints and convex costs such as penalties optimality conditions are stated in terms of a minimaximum principle in which the primal and dual control vectors satisfy a saddle point condition at almost every instant of time this principle is shown to be equivalent to a generalized hamiltonian differential equation in the primal and dual state variables along with a transversality condition that likewise is in hamiltonian form

equivalent subgradient versions of hamiltonian and euler llagrange equations in variational analysis much effort in recent years has gone into generalizing the classical hamiltonian and euler lagrange equations of the calculus of variations so as to encompass problems in optimal control and a greater variety of integrands and constraints these generalizations in which nonsmoothness abounds and gradients are systematically replaced by subgradients have succeeded in furnishing necessary conditions for optimality that reduce to the classical ones in the classical setting but important issues have remained unsettled especially concerning the exact relationship of the subgradient versions of the hamiltonian equations versus those of the euler lagrange equations here it is shown that new tighter subgradient versions of these equations are actually equivalent to each other the theory of epi convergence of convex functions provides the technical basis for this development

differentiability at lateral boundary for fully nonlinear parabolic equations abstract for fully nonlinear uniformly parabolic equations the first derivatives regularity of viscosity solutions at lateral boundary is studied under new dini type conditions for the boundary which is called reifenberg dini conditions and is weaker than usual dini conditions

a global approach to fully nonlinear parabolic problems we consider the general initial boundary value problem 1 u t f x t u du du f x t x t qt 0 t 2 g x t u du g x t x t st 0 t 3 u x 0 h x x where is a bounded open set in rn with sufficiently smooth boundary the problem 1 3 is first reduced to the analogous problem in the space w 4 0 p qt with zero initial condition and f w 2 0 p qt g w 3 1 p 0 p st the resulting problem is then reduced to the problem au 0 where the operator a w 4 0 p qt w 4 0 p qt satisfies condition s this reduction is based on a priori estimates which are developed herein for linear parabolic operators with coefficients in sobolev spaces the local and global solvability of the operator equation au 0 are achieved via topological methods developed by i v skrypnik further applications are also given involving relevant coercive problems as well as galerkin approximations

necessary optimality conditions for nonconvex differential inclusions with endpoint constraints in this paper we derive necessary optimality conditions for optimization problems defined by non convex differential inclusions with endpoint constraints we do this in terms of parametrizations of the convexified form of the differential inclusion and under additional assumptions in terms of the inclusion itself