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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On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems
TL;DR: In this paper, a quasilinear elliptic problem with nonhomogeneous principal part φ was studied and the existence of multiple positive solutions was proved by using the variational arguments in the Orlicz-Sobolev spaces.
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Multiple solutions with precise sign for nonlinear parametric Robin problems
TL;DR: In this paper, a parametric nonlinear Robin problem driven by the p-Laplacian was considered, and it was shown that the problem has at least three nontrivial solutions, two of constant sign and the third nodal.
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A gradient bound for entire solutions of quasi‐linear equations and its consequences
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W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equations
Zongming Guo,Zhitao Zhang +1 more
TL;DR: In this article, it was shown that the local minimizers of a class of functionals in the C1-topology are still their local optimizers in W 1,p 0 (Ω).
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Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
TL;DR: In this article, the first eigenvalue of a highly nonlinear class of elliptic operators, including the pseudo-p-Laplace operator, was derived and the question of symmetry for positive solutions to more general equations was addressed.
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).