w2 p estimates for the parabolic monge ampere equation when u is a solution to the equation ut det dx2u f with f positive continuous and ft satisfying certain growth conditions we establish estimates in l for ut and show that dx2u satisfies uniform interior estimates in lp for 0 p

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

geometric properties of the sections of solutions to the monge ampere equation in this paper we establish several geometric properties of the cross sections of generalized solutions 4 to the monge ampere equation det d2 when the measure t satisfies a doubling property a main result is a characterization of the doubling measures t in terms of a geometric property of the cross sections of 4 this is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations 0 introduction let ri r be a convex function a supporting hyperplane to q at the point xo q xo is an affine function x q xo p x xo such that q x x for all x e r given t 0 a section of 0 at height t is the convex set so xo p t x e r x p ri defined by vq xo p q x xo p x xo vx e rn if e c rn then v e uxee vq x by a classical theorem of aleksandrov the class of sets e such that v e is lebesgue measurable is a o algebra that contains the borel sets and one can define the monge ampere measure associated with q as the borel measure u given by pt v e see ch y the purpose in this paper to analyze in detail several important geometric properties of the sections of the convex function q when its associated monge ampere measure u satisfies a doubling condition the interest in these properties comes from the study of the solutions of the monge ampere equation and its linearizations both elliptic and parabolic and from real harmonic analysis see cl c2 c g1 c g2 and h some of these properties have been used in those references to prove a lemma of besicovitch s type and a calderon zygmund decomposition ir terms of sections which allows us to establish estimates of the solutions to the linearized monge ampere equation also some of these properties imply that r received by the editors june 9 1997 1991 mathematics subject classification primary 35j60 35d10 secondary 26b25

on the invariant symmetries of the d metrics we analyze the symmetries and other invariant qualities of the d metrics type d aligned einstein maxwell solutions with cosmological constant whose debever null principal directions determine shear free geodesic null congruences we recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation and we analyze when these invariant symmetries characterize the family of metrics we show that the subfamily of the kerr nut solutions are those admitting a papapetrou field aligned with the weyl tensor

interior w 2 p estimates for solutions of the monge ampere equation in this work we adapt the techniques developed in c1 to prove interior estimates for solutions of perturbations of the monge ampere equation

killing tensors warped products and the orthogonal separation of the hamilton jacobi equation we study killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the hamilton jacobi equation this work is motivated primarily by the case of spaces of constant curvature where warped products are abundant we first characterize killing tensors which have a natural algebraic decomposition in warped products we then apply this result to show how one can obtain the killing stackel space ks space for separable coordinate systems decomposable in warped products this result in combination with benenti s theory for constructing the ks space of certain special separable coordinates can be used to obtain the ks space for all orthogonal separable coordinates found by kalnins and miller in riemannian spaces of constant curvature next we characterize when a natural hamiltonian is separable in coordinates decomposable in a warped product by showing that the conditions originally given by benenti can be reduced finally we use this characterization and concircular tensors a special type of torsionless conformal killing tensor to develop a general algorithm to determine when a natural hamiltonian is separable in a special class of separable coordinates which include all orthogonal separable coordinates in spaces of constant curvature

on the mean oscillation of the hessian of solutions to the monge ampere equation we give interior a priori estimates for the mean oscillation of second derivatives of solutions to the monge ampere equation detd2u f x with zero boundary values where f x is a non dini continuous function if the modulus of continuity of f x is f r such that limr 0f r log 1 r 0 then d2uvmo

weighted composition operators on the predual and dual banach spaces of beurling algebras on z abstract let v be a weight sequence on z and let be complex valued functions on z such that z z in this paper we study the boundedness compactness and weak compactness of weighted composition operators c on predual banach spaces c 0 z 1 v and dual banach spaces l z 1 v of beurling algebras l 1 z v

on the classification of type d space times we give a classification of the type d space times based on the invariant differential properties of the weyl principal structure our classification is established using tensorial invariants of the weyl tensor and consequently besides its intrinsic nature it is valid for the whole set of the type d metrics and it applies on both vacuum and nonvacuum solutions we consider the cotton zero type d metrics and we study the classes that are compatible with this condition the subfamily of space times with constant argument of the weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the nonexistence of purely magnetic solutions the usefulness of these results is illustrated in characterizing and classifying a family of einstein maxwell solutions our approach permits us to give intrinsic and explicit conditions that label every metric obtaining in this way an operational algorithm to detect them in particular a characterization of the reissner nordstrom metric is accomplished

intrinsic characterization of the variable separation in the hamilton jacobi equation the nonorthogonal separation of variables in the hamilton jacobi equation corresponding to a natural hamiltonian h 12gijpipj v with a metric tensor of any signature is intrinsically characterized by geometrical objects on the riemannian configuration manifold killing vectors killing tensors and killing webs comparisons with previous characterizations and some illustrative examples are given

a localization property of viscosity solutions to the monge ampere equation and their strict convexity the purpose of this note is to show a localization property of convex viscosity solutions to the monge ampere inequality 0 1 2 n are strictly convex

weighted differentiation composition operators from mixed norm spaces to weighted type spaces motivated by the recent paper x zhu products of differentiation composition and multiplication from bergman type spaces to bers spaces integral transform spec funct 18 3 2007 223 231 we study the boundedness and compactness of the weighted differentiation composition operator d f u n f z u z f n f z where u is a holomorphic function on the unit disk d f is a holomorphic self map of d and email protected n 0 from the mixed norm space h p q f where p q 0 and f is normal to the weighted type space h m or the little weighted type space h m 0 for the case of the weighted bergman space a a p p 1 some bounds for the essential norm of the operator are also given

on the geometry of killing and conformal tensors the second order killing and conformal tensors are analyzed in terms of their spectral decomposition and some properties of the eigenvalues and the eigenspaces are shown when the tensor is of type i with only two different eigenvalues the condition to be a killing or a conformal tensor is characterized in terms of its underlying almost product structure a canonical expression for the metrics admitting these kinds of symmetries is also presented the space time cases 1 3 and 2 2 are analyzed in more detail starting from this approach to killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum petrov bel type d solutions is offered a generalization of these results to a wider family of type d space times is also obtained

estimates in the generalized campanato john nirenberg spaces for fully nonlinear elliptic equations we establish estimates in bmo and campanato john nirenberg spaces bmo for the second derivatives of solutions to the fully nonlinear elliptic equation f d2u x f x

weighted composition operators from the weighted bergman space to the weighted hardy space on the unit ball we investigate the weighted composition operator from the weighted bergman space into the weighted hardy space on the unit ball as a consequence of the investigation we also give a characterization for the boundedness and compactness of the operator whose the target space is the hardy space

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

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

first integrals of holonomic systems without noether symmetries a theorem is proved that determines the first integrals of the form i kab t q qaqb ka t q qa k t q of autonomous holonomic systems using only the collineations of the kinetic metric that is defined by the kinetic energy or the lagrangian of the system it is shown how these first integrals can be associated via the inverse noether theorem with a gauged weak noether symmetry which admits the given first integral as a noether integral it is shown also that the associated noether symmetry is possible to satisfy the conditions for a hojman or a form invariance symmetry therefore the so called non noetherian first integrals are gauged weak noether integrals the application of the theorem requires a certain algorithm due to the complexity of the special conditions involved we demonstrate this algorithm by a number of solved examples we choose examples from published works in order to show that our approach produces new first integrals not found before with the standard methods

w 2 p estimates for the linearized monge ampere equation let c r be a strictly convex domain and let c 2 be a convex function such that det d 2 0 and c 0 depending only on n a a and dist such that for all solutions u c 2 to the equation l u f

sharp regularity results on second derivatives of solutions to the monge ampere equation with vmo type data we establish interior estimates for lp norms orlicz norms and mean oscillation of second derivatives of solutions to the monge ampere equation det d2u f x with zero boundary value where f x is strictly positive bounded and satisfies a vmo type condition these estimates develop the regularity theory of the monge ampere equation in vmo type spaces our orlicz estimates also sharpen caffarelli s celebrated w2 p estimates 2008 wiley periodicals inc

weighted composition operators from bergman privalov type spaces to weighted type spaces on the unit ball abstract motivated by recent paper x zhu appl math comput 215 12 2010 4340 4346 we characterize the boundedness and compactness of weighted composition operators from the bergman privalov type space to weighted type and the little weighted type space on the unit ball in c n