TITLE

On coercivity and regularity for linear elliptic systems

AUTHOR(S)
Zhang, Kewei
PUB. DATE
January 2011
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2011, Vol. 40 Issue 1/2, p65
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We introduce a nonlinear method to study a 'universal' strong coercivity problem for monotone linear elliptic systems by compositions of finitely many constant coefficient tensors satisfying the Legendre-Hadamard strong ellipticity condition. We give conditions and counterexamples for universal coercivity. In the case of non-coercive systems we give examples to show that the corresponding variational integral may have infinitely many nowhere C minimizers on their supports. For some universally coercive systems we also present examples with affine boundary values which have nowhere C solutions.
ACCESSION #
55471505

 

Related Articles

  • Global Conjugation of Solutions of a Hyperbolic Problem along an Unknown Contact Boundary. Andrusyak, R.; Burdeina, N.; Kyrylych, V. // Journal of Mathematical Sciences;Jun2013, Vol. 191 Issue 3, p329 

    We consider the problem of local and global solvability of a nonlinear problem with a free (unknown) line of discontinuity of initial data for a hyperbolic system of first-order quasilinear equations with two independent variables. For the problem to be globally solvable, one should additionally...

  • Periodic solutions for nonlinear telegraph equation via elliptic regularization. de Araújo, G. M.; Gúzman, R. B.; de Menezes, Silvano B. // Computational & Applied Mathematics;2009, Vol. 28 Issue 2, p135 

    In this work we are concerned with the existence and uniqueness of T-periodic weak solutions for an initial-boundary value problem associated with nonlinear telegraph equations type in a domain Q ⊂ ℝN. Our arguments rely on elliptic regularization technics, tools from classical...

  • QUASI-CONCAVITY FOR SEMILINEAR ELLIPTIC EQUATIONS WITH NON-MONOTONE AND ANISOTROPIC NONLINEARITIES. Greco, Antonio // Boundary Value Problems;2006, p1 

    A boundary-value problem for a semilinear elliptic equation in a convex ring is considered. Under suitable structural conditions, any classical solution u lying between its (constant) boundary values is shown to decrease along each ray starting from the origin, and to have convex level surfaces.

  • Existence of solutions of elliptic boundary value problems with mixed type nonlinearities. Mao, Anmin; Zhu, Yan; Luan, Shixia // Boundary Value Problems;2012, Vol. 2012 Issue 1, p1 

    We study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities: [Equation not available: see fulltext.] where [InlineEquation not available: see fulltext.]. We consider the problem in a different case: [InlineEquation not...

  • MONOTONE FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHMS AND APPLICATIONS TO NONLINEAR SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS. Boglaev, Igor; Hardy, Matthew // Advances in Difference Equations;2006, p1 

    This paper deals with monotone finite difference iterative algorithms for solving nonlinear singularly perturbed reaction-diffusion problems of elliptic and parabolic types. Monotone domain decomposition algorithms based on a Schwarz alternating method and on box-domain decomposition are...

  • THE METHOD OF UPPER AND LOWER SOLUTIONS FOR SECOND-ORDER NON-HOMOGENEOUS TWO-POINT BOUNDARY-VALUE PROBLEM. Mei Jia; Xiping Liu // Electronic Journal of Differential Equations;2007, Vol. 2007, p1 

    This paper studies the existence and uniqueness of solutions for a type of second-order two-point boundary-value problem depending on the first-order derivative through a non-linear term. By constructing a special cone and using the upper and lower solutions method, we obtain the sufficient...

  • Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems. Cianchi, Andrea; Maz'ya, Vladimir // Archive for Rational Mechanics & Analysis;Apr2014, Vol. 212 Issue 1, p129 

    Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed....

  • POSITIVE SOLUTIONS FOR INDEFINITE INHOMOGENEOUS NEUMANN ELLIPTIC PROBLEMS. Il'Yasov, Yavdat; Runst, Thomas // Electronic Journal of Differential Equations;2003, Vol. 2003, p1 

    We consider a class of inhomogeneous Neumann boundary-value problems on a compact Riemannian manifold with boundary where indefinite and critical nonlinearities are included. We introduce a new and, in some sense, more general variational approach to these problems. Using this idea we prove new...

  • Plane strain problem for an incompressible nonlinearly elastic solid. Bondar', V. D. // Journal of Applied Mechanics & Technical Physics;Mar2009, Vol. 50 Issue 2, p352 

    The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity are derived in terms of the elastic potential....

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics