Journal ArticleDOI
Boundary regularity for solutions of degenerate elliptic equations
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On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x andu, Du) = 0 avec des conditions aux limites conormales et de Dirichlet.Abstract:
On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x,u,Du)=0 avec des conditions aux limites conormales et de Dirichletread more
Citations
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Variational approach to noncoercive systems of elliptic variational inequalities via trapping region
TL;DR: In this article, a variational approach of the non-coercive elliptic system of variational inequalities has been proposed to transform the given variational system into an associated truncated system to which variational methods can be applied, which can be characterized as the critical points of a suitably constructed energy functional.
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Multiple solutions for superlinear $p$-Laplacian Neumann problems
TL;DR: In this article, the authors prove the existence of multiple solutions with precise sign information for a Neumann problem driven by the $p$-Laplacian differential operator with a ($p-1$)-superlinear term which does not satisfy the Ambrosetti--Rabinowitz condition.
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Multiple solutions to p-Laplacian problems with concave nonlinearities
Linsong Shi,Xiaojun Chang +1 more
TL;DR: In this article, the p-Laplacian type elliptic problems with concave nonlinearities were studied and three nontrivial solutions were established using some asymptotic behavior of f at zero and infinity.
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Gradient estimates for the strong $p(x)$-Laplace equation
Chao Zhang,Xia Zhang,Shulin Zhou +2 more
TL;DR: In this article, the authors study nonlinear elliptic equations of strong $p(x)$-Laplacian type to obtain an interior Calderon-Zygmund type estimate by finding a correct regularity assumption on the variable exponent.
On sign-changing andmultiple solutions of the p-Laplacian $
TL;DR: In this paper, the pseudo-gradient vector field in W 1;p 0 ðOÞ was constructed, by which they obtained the pseudo gradient vector field with W 1,p 0 OÞ
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Regularity for a more general class of quasilinear elliptic equations
TL;DR: On considere des solutions u∈H 1,p (Ω)∧L ∞ ( Ω) (1
Journal ArticleDOI
C1 + α local regularity of weak solutions of degenerate elliptic equations
TL;DR: In this article, the local C(1 + Alpha) nature of weak solutions of elliptic equations of the type (1.1) in the introduction under the degeneracy (or singularity) assumptions (A sub 1)-(A sub 3).