a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

an iterative substructuring algorithm for two dimensional problems in h curl a domain decomposition algorithm similar to classical iterative substructuring algorithms is presented for two dimensional problems in the space h 0 mbox curl omega it is defined in terms of a coarse space and local subspaces associated with individual edges of the subdomains into which the domain of the problem has been subdivided the algorithm differs from others in three basic respects first it can be implemented in an algebraic manner that does not require access to individual subdomain matrices or a coarse discretization of the domain this is in contrast to algorithms of the bddc feti dp and classical two level overlapping schwarz families second favorable condition number bounds can be established over a broader range of subdomain material properties than in previous studies third we are able to develop theory for quite irregular subdomains and bounds for the condition number of our preconditioned conjugate gradient algorithm which depend only on a few geometric parameters the c

weighted estimates for generalized steady stokes systems in nonsmooth domains we consider a generalized steady stokes system with discontinuous coefficients in a nonsmooth domain when the inhomogeneous term belongs to a weighted lq space for 2 q we prove the global weighted lq estimates for the gradient of the weak solution and an associated pressure under the assumptions that the coefficients have small bounded mean oscillation semi norms and the domain is sufficiently flat in the reifenberg sense on the other hand a given weight is assumed to belong to a muckenhoupt class our result generalizes the global w1 q estimate of calderon zygmund with respect to the lebesgue measure for the stokes system in a lipschitz domain

poincare meets korn via maxwell extending korn s first inequality to incompatible tensor fields for a bounded domain r3 r3 with lipschitz boundary and some relatively open lipschitz subset t t of we prove the existence of some c 0c 0 such that equation 0 1 c t l2 r3 3 symt l2 r3 3 curlt l2 r3 3 holds for all tensor fields in h curl h curl i e for all square integrable tensor fields t r3 3t r3 3 with square integrable generalized rotation curlt r3 3 having vanishing restricted tangential trace on t t if t t 0 1 still holds at least for simply connected and for all tensor fields t h curl t h curl which are l2 l2 perpendicular to so 3 so 3 i e to all skew symmetric constant tensors here both operations curl and tangential trace are to be understood row wise for compatible tensor fields t vt v 0 1 reduces to a non standard variant of the well known korn s first inequality in r3r3 namely c v l2 r3 3 sym v l2 r3 3 for all vector fields v h1 r3 v h1 r3 for which vn vn n 1 3n 1 3 are normal at t t on the other hand identifying vector fields v h1 r3 v h1 r3 having the proper boundary conditions with skew symmetric tensor fields t 0 1 turns to poincare s inequality since 2c v l2 r3 c t l2 r3 3 curlt l2 r3 3 2 v l2 r3 therefore 0 1 may be viewed as a natural common generalization of korn s first and poincare s inequality from another point of view 0 1 states that one can omit compatibility of the tensor field t at the expense of measuring the deviation from compatibility through curl t decisive tools for this unexpected estimate are the classical korn s first inequality helmholtz decompositions for mixed boundary conditions and the maxwell estimate

on the inequalities of babuska aziz friedrichs and horgan payne the equivalence between the inequalities of babuska aziz and friedrichs for sufficiently smooth bounded domains in the plane was shown by horgan and payne 30 years ago we prove that this equivalence and the equality between the associated constants is true without any regularity condition on the domain for the horgan payne inequality which is an upper bound of the friedrichs constant for plane star shaped domains in terms of a geometric quantity known as the horgan payne angle we show that it is true for some classes of domains but not for all bounded star shaped domains we prove a weaker inequality that is true in all cases

solvability of the divergence equation implies john via poincare inequality abstract let r 2 be a bounded simply connected domain we show that for a fixed every p 1 the divergence equation div v f is solvable in w 0 1 p 2 for every f l 0 p if and only if is a john domain if and only if the weighted poincare inequality u x u q d x c u x q dist x q d x holds for some every q 1 this gives a positive answer to a question raised by russ 2013 in the case of bounded simply connected domains in higher dimensions similar results are proved under some additional assumptions on the domain in question

solutions of the divergence operator on john domains if rn is a bounded domain the existence of solutions u w01 p of divu f for f lp with vanishing mean value and 1 p is a basic result in the analysis of the stokes equations it is known that the result holds when is a lipschitz domain and that it is not valid for domains with external cusps in this paper we prove that the result holds for john domains our proof is constructive the solution u is given by an explicit integral operator acting on f to prove that u w01 p we make use of the calderon zygmund singular integral operator theory and the hardy littlewood maximal function for domains satisfying the separation property introduced in s buckley p koskela sobolev poincare implies john math res lett 2 5 1995 577 593 and 1 p n we also prove a converse result thus characterizing in this case the domains for which a continuous right inverse of the divergence exists in particular our result applies to simply connected planar domains because they satisfy the separation property

runge kutta methods for hyperbolic conservation laws with stiff relaxation terms underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well resolved we design a second order runge kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit which thus is able to capture the correct physical behaviors with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved

domain decomposition for less regular subdomains overlapping schwarz in two dimensions in the theory of domain decomposition methods it is often assumed that each subdomain is the union of a small set of coarse triangles or tetrahedra in this study extensions to the existing theory which accommodate subdomains with much less regular shapes are presented the subdomains are required only to be john domains attention is focused on overlapping schwarz preconditioners for problems in two dimensions with a coarse space component of the preconditioner which allows for good results even for coefficients which vary considerably it is shown that the condition number of the domain decomposition method is bounded by c 1 h delta 1 log h h 2 where the constant c is independent of the number of subdomains and possible jumps in coefficients between subdomains numerical examples are provided which confirm the theory and demonstrate very good performance of the method for a variety of subregions including those obtained when a mesh partitioner is used for the domain decomposition

some remarks on g functors and the brauer morphism keywords finite group g functor restriction maps transfer maps mackey s formula frobenius reciprocity brauer morphism defect base nilpotent ideal burnside ring idempotent formula induction formula symmetric g functor character ring green ring reference ctg article 1988 003 record created on 2008 12 16 modified on 2017 05 12

new hybrid runge kutta methods for unsteady reactive flow simulation applications the applicability is examined of the new hybrid runge kutta methods derived in the companion paper by specifically analyzing both nonstiff and stiff system of equations that represent multidimensional reactive flows in a reactive flow simulation the standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system the new hybrid runge kutta schemes are suitable for this task because the time step size is controlled by the courant condition whereas the stiffness is treated by an unconditionally stable method this set of methods also meets the modern computing needs of high order accuracy and low storage requirement a representative scheme is used to simulate a series of combustion problems that include model equations with stiff sources and multidimensional detonations with complex chemical kinetics

elementary construction of the quiver of the mackey algebra for groups with cyclic normal p sylow subgroup through recent investigations of j thrvenaz and p j webb 4 8 the concept of mackey functors being originally introduced by j a green 3 and studied by a w m dress t yoshida h sasaki and others has regained considerable interest an important reason for this is i new interpretation of a conjecture of aiperin in terms of mackey functors in 8 using results of 7 given a commutative ring 4 by its definition it is immediate that the category of mackey functors over 4 for a finite group g is an abelian category even that it is the category of 4 representations of a quiver with relations 8 namely a mackey functor for g associates to each subgroup of g a module and moreover certain linear maps between these spaces satisfying certain relations involving g thus a mackey functor for g can be interpreted as a module over a path algebra of a quiver with relations the so called mackey algebra 6 9 the main difference to the usual representation theory of quivers and thus the main problem of interpreting mackey functors as such representations lies in the fact that the maps between these spaces do not lie in the radical of this path algebra and this path algebra is not basic in general so it is a natural problem to compute the quiver in the usual sense for the category of mackey functors for a group g in particular in the case where 4 is a field of characteristic p dividing the order of g the question of when there are up to isomorphism only finitely many indecomposable mackey functors for g led to recent investigations of thrvenaz and webb solving this problem in general and it also led to the investigations we present in this paper which presents in a special situation namely if g has a normal cyclic p sylow subgroup an explicit computation of the quiver of the now so called mackcy algebra by definition the mackey algebra is the basic algebra whose category of finitely generated

weighted lq estimates for stationary stokes system with partially bmo coefficients abstract we prove the unique solvability of solutions in sobolev spaces to the stationary stokes system on a bounded reifenberg flat domain when the coefficients are partially bmo functions i e locally they are merely measurable in one direction and have small mean oscillations in the other directions using this result we establish the unique solvability in muckenhoupt type weighted sobolev spaces for the system with partially bmo coefficients on a reifenberg flat domain we also present weighted a priori l q estimates for the system when the domain is the whole euclidean space or a half space

homogenization of the compressible navier stokes equations in domains with very tiny holes abstract we consider the homogenization problem of the compressible navier stokes equations in a bounded three dimensional domain perforated with very tiny holes as the number of holes increases to infinity we show that if the size of the holes is small enough the homogenized equations are the same as the compressible navier stokes equations in the homogeneous domain domain without holes this coincides with the previous studies for the stokes equations and the stationary navier stokes equations it is the first result of this kind in the instationary barotropic compressible setting the main technical novelty is the study of the bogovski operator in non lipschitz domains

an analysis of a feti dp algorithm on irregular subdomains in the plane in the theory for domain decomposition algorithms of the iterative substructuring family each subdomain is typically assumed to be the union of a few coarse triangles or tetrahedra this is an unrealistic assumption in particular if the subdomains result from the use of a mesh partitioner in which case they might not even have uniformly lipschitz continuous boundaries the purpose of this study is to derive bounds for the condition number of these preconditioned conjugate gradient methods which depend only on a parameter in an isoperimetric inequality two geometric parameters characterizing john and uniform domains and the maximum number of edges of any subdomain a related purpose is to explore to what extent well known technical tools previously developed for quite regular subdomains can be extended to much more irregular subdomains some of these results are valid for any john domain while an extension theorem which is needed in this study requires that the subdomains have complements which are uniform the results so far are complete only for problems in two dimensions details are worked out for a feti dp algorithm and numerical results support the findings some of the numerical experiments illustrate that care must be taken when selecting the scaling of the preconditioners in the case of irregular subdomains

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

self improving properties of inequalities of poincare type on measure spaces and applications abstract we show that the self improving nature of poincare estimates persists for domains in rather general measure spaces we consider both weak type and strong type inequalities extending techniques of b franchi c perez and r wheeden as an application in spaces of homogeneous type we derive global poincare estimates for a class of domains with rough boundaries that we call john domains and we show that such domains have the requisite properties this class includes john or boman domains as well as s john domains further applications appear in a companion paper

korn type inequalities in orlicz spaces abstract we exhibit balance conditions between a young function a and a young function b for a korn type inequality to hold between the l b norm of the gradient of vector valued functions and the l a norm of its symmetric part in particular we extend a standard form of the korn inequality in l p with 1 p and an orlicz version involving a young function a satisfying both the 2 and the 2 condition

stokes theorem for domains with fractal boundary in this paper integrals of second kind over a rectifiable curve or a piecewise smooth surface are extended to continuous fractal curves and surfaces theorems for the existence of these integrals are proved green s gauss and stokes theorems are developed for domains with fractal boundaries

the dade group of mackey functors for p groups abstract we introduce endo permutation mackey functors and the mackey dade group of a p group and study their basic properties we exhibit relations between the mackey dade group of a finite p group p and the dade groups of the weyl groups of all subgroups of p as a result we show that the mackey dade group tensored with q over z is the kernel of the linearization map for mackey functors introduced by the author

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

convergence rates and w1 p estimates in homogenization theory of stokes systems in lipschitz domains abstract concerned with the stokes systems with rapidly oscillating periodic coefficients we mainly extend the recent works in 19 20 to those in term of lipschitz domains the arguments employed here are quite different from theirs and the basic idea comes from 37 originally motivated by 23 27 33 we obtain an almost sharp o e ln r 0 e convergence rate in l 2 space and a sharp o e error estimate in l 2 d d 1 space by a little stronger assumption under the dimensional condition d 2 we also establish the optimal o e convergence rate on pressure terms in l 2 space then utilizing the convergence rates we can derive the w 1 p estimates uniformly down to microscopic scale e without any smoothness assumption on the coefficients where 1 p 1 2 1 2 d and is a positive constant independent of e combining the local estimates based upon vmo coefficients consequently leads to the uniform w 1 p estimates here the proofs do not rely on the well known compactness methods

new hybrid runge kutta methods for unsteady reactive flow simulation in the numerical simulation of transient reacting flow standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system to circumvent this new hybrid implicit explicit methods proposed treat the stiffness whereas the underlying time step control is governed by the courant stability criterion because the coefficients of both explicit and implicit operations are entirely determined by solving the necessary conditions of accuracy and l stability without any extra assumptions the methods are more generalized than other similar methods in the literature two families of semi implicit runge kutta schemes are developed for split differential equations in the form of u f t u g t u where f is treated explicitly and g is simultaneously treated implicitly like the rest of all the developed schemes a low storage family of semi implicit schemes is also derived to be globally high order accurate and l stable for implicit calculations in a companion paper yoh j j and zhong x new hybrid runge kutta methods for unsteady reactive flow simulation applications aiaa journal v ol 42 no 8 2004 pp 1601 1611 the new schemes are tested to solve a wide range of applications in high speed flow physics involving combustion

a decomposition technique for integrable functions with applications to the divergence problem abstract let r n be a bounded domain that can be written as t t where t t is a countable collection of domains with certain properties in this work we develop a technique to decompose a function f l 1 with vanishing mean value into the sum of a collection of functions f t f t t subordinated to t t such that supp f t f t t and f t f t 0 as an application we use this decomposition to prove the existence of a solution in weighted sobolev spaces of the divergence problem div u f and the well posedness of the stokes equations on holder domains and some other domains with an external cusp arbitrarily narrow we also consider arbitrary bounded domains the weights used in each case depend on the type of domain

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

improved poincare inequalities with weights abstract in this paper we prove that if r n is a bounded john domain the following weighted poincare type inequality holds inf a r f x a l q w 1 c f x d x l p w 2 where f is a locally lipschitz function on d x denotes the distance of x to the boundary of the weights w 1 w 2 satisfy certain cube conditions and 0 1 depends on p q and n this result generalizes previously known weighted inequalities which can also be obtained with our approach

korn inequality on irregular domains abstract in this paper we study the weighted korn inequality on some irregular domains e g s john domains and domains satisfying quasihyperbolic boundary conditions examples regarding sharpness of the korn inequality on these domains are presented moreover we show that korn inequalities imply certain poincare inequality

a conformal korn inequality on holder domains abstract in this paper we derive a sharp conformal korn inequality on holder domains we also provide an example for the sharpness of the result this shows that the conformal korn inequality has a different behavior than the classical one on holder domains

estimates for green functions of stokes systems in two dimensional domains abstract we prove the existence and pointwise bounds of the green functions for stationary stokes systems with measurable coefficients in two dimensional domains we also establish pointwise bounds of the derivatives of the green functions under a regularity assumption on the l 1 mean oscillations of the coefficients

an overlapping schwarz algorithm for almost incompressible elasticity overlapping schwarz methods are extended to mixed finite element approximations of linear elasticity which use discontinuous pressure spaces the coarse component of the preconditioner is based on a low dimensional space previously developed for scalar elliptic problems and a domain decomposition method of iterative substructuring type i e a method based on nonoverlapping decompositions of the domain while the local components of the preconditioner are based on solvers on a set of overlapping subdomains a bound is established for the condition number of the algorithm which grows in proportion to the logarithm of the number of degrees of freedom in individual subdomains and essentially to the third power of the relative overlap between the overlapping subdomains and which is independent of the poisson ratio as well as jumps in the lame parameters across the interface between the subdomains a positive definite reformulation of the discrete problem makes the use of the standard preconditioned conjugate gradient method straightforward numerical results which include a comparison with problems of compressible elasticity illustrate the findings

quasilinear schrodinger equations i small data and quadratic interactions abstract in this article we prove local well posedness in low regularity sobolev spaces for general quasilinear schrodinger equations these results represent improvements in the small data regime of the pioneering works by kenig ponce vega and kenig ponce rolvung vega where viscosity methods were used to prove existence of solutions in very high regularity spaces our arguments here are purely dispersive the function spaces in which we show existence are constructed in ways motivated by the results of mizohata ichinose doi and others including the authors

categorifying induction formulae via divergent series abstract we show how to get explicit induction formulae for finite group representations and more generally for rational green functors by summing a divergent series over dwyer s subgroup and centralizer decomposition spaces this results in formulae with rational coefficients the former space yields a well known induction formula the latter yields a new one as essentially immediate corollaries of the existing literature we get similar formulae in group cohomology and stable splittings of classifying spaces

g algebras jacobson radical and almost split sequences keywords finite group indecomposable kg module sas sequence almost split exact sequences restriction relative jacobson radicals local criterion multiplicity module vertex source indecomposable projective module twisted group algebra induction reference ctg article 1988 006doi 10 1007 bf01393690 record created on 2008 12 16 modified on 2017 05 12