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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Journal ArticleDOI
Existence of Multiple Solutions for Nonlinear Dirichlet Problems with a Nonhomogeneous Differential Operator
TL;DR: In this paper, the authors consider nonlinear elliptic problems driven by a nonhomogeneous nonlinear differential operator and prove two multiplicity results establishing three nontrivial smooth solutions.
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Large solutions to an anisotropic quasilinear elliptic problem
TL;DR: In this article, the authors considered existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem and proved that the necessary and sufficient condition for the existence of a solution is r > max{p−1, q−1}.
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Нелокальные исследования бифуркаций решений нелинейных эллиптических уравнений@@@Non-local investigation of bifurcations of solutions of non-linear elliptic equations
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Nonlinear Robin problems with indefinite potential
TL;DR: In this article, the authors considered a nonlinear Robin problem driven by the p -Laplacian plus an indefinite potential and proved two multiplicity theorems with sign information for all the solutions.
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On the uniqueness of the solution of a nonlinear filtration problem through a porous medium
TL;DR: In this paper, a fluid flow through a porous medium governed by a nonlinear Darcy's law was studied and the continuity of the free boundary and the uniqueness of the solution were established.
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
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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).