the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

mindlin s problem for an anisotropic piezoelectric half space with general boundary conditions this paper considers mindlin s problem in an anisotropic and piezoelectric halfspace with general boundary conditions including 16 different sets of surface conditions the green s function due to

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

equations du type de monge ampere sur les varietes hermitiennes compactes resume soit x g une variete hermitienne compacte si c 2 x soit m det etude d equations de la forme m f x ou f c tx r est une fonction partout strictement positive ayant une croissance exponentielle en et majoree par une puissance de la norme du gradient de let x g be a hermitian compact manifold for c 2 x let m det study of equations of the form m f x where f c tx r is an everywhere strictly positive function with an exponential growth in and which is bounded by a power of the norm of the gradient of

identification of symmetry type of linear elastic stiffness tensor in an arbitrarily orientated coordinate system abstract we develop a method through the mirror plane mp to identify the symmetry type of linear elastic stiffness tensor whose components are given with respect to an arbitrarily oriented coordinate system the method is based on the irreducible decomposition of high order tensor into a set of deviators and the multipole representation of a deviator into a scalar and a unit vector set since a unit vector depends on two euler angles we can illustrate the mp normals of the elastic tensor as zeros of a characteristic function on a unit disk and identify its symmetry immediately which is clearer and simpler than the methods proposed before furthermore by finding the common mps of three unit vector sets using fortran recipes we can also analytically recognize the symmetry type first and then recover the natural coordinate system associated with the linear elastic tensor the structures of linear elastic stiffness tensors of real materials with all possible anisotropies are investigated in detail

a local index theorem for non kahler manifolds on considere des conditions suffisantes pour qu un theoreme d indice local soit vrai pour un operateur de dirac associe a une connexion qui ne coincide pas necessairement avec la connexion de levi civita l

distance of a stiffness tetrad to the symmetry classes of linear elasticity abstract in the scope of linear anisotropic elasticity the fourth order elasticity tensor or tetrad has to be identified this can be done either by measurements or by numerical simulations an important task is then to identify a given tetrad probably with some experimental or numerical scattering with one of the symmetry classes for this purpose one needs a distance function between a given tetrad and the class of all tetrads with a particular symmetry which is zero if the tetrad obeys this symmetry or non zero otherwise in this paper we present a fast method to solve these problems we firstly introduce the 8th order projectors that map any stiffness tetrad into the part that is invariant under the action of a specific fixed symmetry group for this purpose we consider the seven out of the eight symmetry classes that are distinguishable in linear elasticity secondly since the symmetry axes of the specific stiffness tensor under consideration is generally not aligned with the used tensorial basis of the projector we need to rotate the sample stiffness the optimal orientation is obtained when the distance between the rotated stiffness and the rotated and projected stiffness is minimal thus we need to apply only linear mappings and minimize over three euler angles the latter is quite simple as the domain of the euler angles is periodic and the number of local minima is limited this procedure has the advantage that it is applicable in an algorithmic manner and does not require an a priori identification of symmetry planes symmetry axes or component symmetries which are only apparent under special choices for the tensorial basis

viscosity solutions to complex hessian equations we study viscosity solutions to complex hessian equations in the local case we consider a bounded domain in cn the standard kahler form in cn and 1 m n under some suitable conditions on f g we prove that the equation ddc m n m f x n g on admits a unique viscosity solution modulo the existence of subsolution and supersolution if moreover the datum is holder continuous then so is the solution in the global case let x be a compact hermitian homogeneous manifold where is an invariant hermitian metric not necessarily kahler we prove that the equation ddc m n m f x n has a unique viscosity solution under some natural conditions on f

generalized cowin mehrabadi theorems and a direct proof that the number of linear elastic symmetries is eight abstract the cowin mehrabadi theorem is generalized to allow less restrictive and more flexible conditions for locating a symmetry plane in an anisotropic elastic material the generalized theorems are then employed to prove that the number of linear elastic symmetries is eight the proof starts by imposing a symmetry plane to a triclinic material and after new elastic symmetries are found another symmetry plane is imposed this process exhausts all possibility of elastic symmetries and shows that there are only eight elastic symmetries at each stage when a new symmetry plane is added explicit results are obtained for the locations of the new symmetry plane that lead to a new elastic symmetry it takes as few as three and at most five symmetry planes to reduce a triclinic material which has no symmetry plane to an isotropic material for which any plane is a symmetry plane

a variational theory of the hessian equation by studying a negative gradient flow of certain hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous hessian equations to achieve this we derive uniform first and second order a priori estimates for the elliptic and parabolic hessian equations our results generalize well known results for semilinear elliptic equations and the monge ampere equation c 2001 john wiley sons inc

collapsing of the chern ricci flow on elliptic surfaces we investigate the chern ricci flow an evolution equation of hermitian metrics generalizing the kahler ricci flow on elliptic bundles over a riemann surface of genus greater than one we show that starting at any gauduchon metric the flow collapses the elliptic fibers and the metrics converge to the pullback of a kahler einstein metric from the base some of our estimates are new even for the kahler ricci flow a consequence of our result is that on every minimal non kahler surface of kodaira dimension one the chern ricci flow converges in the sense of gromov hausdorff to an orbifold kahler einstein metric on a riemann surface

complex monge ampere equations and totally real submanifolds abstract we study the dirichlet problem for complex monge ampere equations in hermitian manifolds with general non pseudoconvex boundary our main result theorem 1 1 extends the classical theorem of caffarelli kohn nirenberg and spruck in c n we also consider the equation on compact manifolds without boundary attempting to generalize yau s theorems in the kahler case as applications of the main result we study some connections between the homogeneous complex monge ampere hcma equation and totally real submanifolds and a special dirichlet problem for the hcma equation related to donaldson s conjecture on geodesics in the space of kahler metrics

determination of the symmetries of an experimentally determined stiffness tensor application to acoustic measurements abstract for most materials the symmetry group is known a priori and deduced from the realization process this allows many simplifications for the measurements of the stiffness tensor we deal here with the case where the symmetry is a priori unknown as for biological or geological materials or when the process makes the material symmetry axis uncertain some composites monocrystals the measurements are then more complicated and the raw stiffness tensor obtained does not exhibit any symmetry in the voigt s matrical form as it is expressed in the arbitrarily chosen specimen s base a complete ultrasonic measurement of this stiffness tensor from redundant measurements is proposed in a second time we show how to make a plane symmetry pole figure able to give visual information about the quasi symmetries of a raw stiffness tensor determined by any measurement method finally we introduce the concept of distance from a raw stiffness tensor to one of the eight symmetry classes available for a stiffness tensor the method provides the nearest tensor to the raw stiffness tensor possessing a chosen symmetry class with its associated natural symmetry base

maxwell s multipole representation of traceless symmetric tensors and its application to functions of high order tensors it is known from the theory of group representations that a general tensor can be expressed as a sum of traceless symmetric tensors in this paper based on sylvester9s theorem it is shown that a general traceless symmetric tensor of any finite order m in three dimensions can be expressed as the traceless symmetric part of tensor product of m unit vectors called the multipoles multiplied by a positive scalar the above two basic structures of tensors allow us to easily give complete and irreducible representations for tensor functions with high order tensor variables since those for tensor functions of vectors are well established in the literature examples are given for scalar valued functions of a single fourth order tensor of the elastic type and of a number of vectors and second order tensors in 1970 backus gave an alternative proof of sylvester9s theorem which shows how to compute the multipoles since backus9s result is not so well known to the community of researchers working on continuum mechanics in the present paper a direct without using sylvester9s theorem and constructive establishment of maxwell9s multipole representation is provided which is closer in spirit to a more modern approach to this topic

on meije and sccs infinite sum operators vs non guarded definitions une des principales differences actuellement entre meije et sccs se trouve dans les limites que le calcul precedent etablit a l interieur de sa syntaxe sur la creation de choix de comportement inifini a chaque point du processus

deformation limits of projective manifolds hodge numbers and strongly gauduchon metrics this paper is intended to start a series of works aimed at proving that if in a smooth complex analytic family of compact complex manifolds all the fibres except one are supposed to be projective then the remaining limit fibre must be moishezon a new method of attack whose starting point originates in demailly s work is introduced while we hope to be able to address the general case in the near future two important special cases are established here the one where the hodge numbers h0 1 of the fibres are supposed to be locally constant and the one where the limit fibre is assumed to be a strongly gauduchon manifold the latter is a rather weak metric assumption giving rise to a new rather general class of compact complex manifolds that we hereby introduce and whose relevance to this type of problems we underscore

symmetry types of the piezoelectric tensor and their identification the third order linear piezoelectricity tensor seems to be simpler than the fourth order linear elasticity one yet its total number of symmetry types is larger than the latter and the exact number

gauduchon metrics with prescribed volume form we prove that on any compact complex manifold one can find gauduchon metrics with prescribed volume form this is equivalent to prescribing the chern ricci curvature of the metrics and thus solves a conjecture of gauduchon from 1984

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

algebraic calculi of processes and net expressions abstract it is shown that the meije algebra of processes can be expressed in a flow algebra the algebra of net expressions we then use this fact to derive a normal form for the calculus

the monge ampere equation on almost complex manifolds we study the dirichlet problem for the monge ampere equation on almost complex manifolds we obtain the existence of the unique smooth solution in strictly pseudoconvex domains

fully non linear elliptic equations on compact hermitian manifolds we derive a priori estimates for solutions of a general class of fully non linear equations on compact hermitian manifolds our method is based on ideas that have been used for different specific equations such as the complex monge ampere hessian and inverse hessian equations as an application we solve a class of hessian quotient equations on kahler manifolds assuming the existence of a suitable subsolution the method also applies to analogous equations on compact riemannian manifolds