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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Dissertation
Existence et multiplicité de solutions pour des problèmes elliptiques avec croissance critique dans le gradient
Fernández Sánchez,José Antonio +1 more
TL;DR: In this paper, the authors introduce the notion of six chapitres, i.e., the sujet de these, composed of six different perspectives of recherche, and present a set of results on the existence and non-existence of solutions for different types of equations.
Journal ArticleDOI
Regularity of quasi-linear equations with Hörmander vector fields of step two
TL;DR: In this paper , the authors established the full interior regularity theory of quasi-linear equations with p-Laplacian type growth condition and showed that a weak solution of the equation is locally C 1,α.
Journal ArticleDOI
Gradient estimates for nonlinear elliptic equations with vanishing Neumann data in quasiconvex domains
Sun-Sig Byun,Hun Kwon +1 more
TL;DR: In this article, the conormal derivative problem for an elliptic equation of p-Laplacian type with discontinuous coefficients in a non-smooth domain was studied and the minimal assumptions necessary to have the nonlinear Calderon-Zygmund theory for such problem were obtained.
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Estimates and rigidity for stable solutions to some nonlinear elliptic problems
TL;DR: In this article, the authors studied the regularity of stable solutions to a nonlinear equation involving the p-Laplacian in a bounded domain and proved the boundedness of stable solution under a new condition on n and p, which is optimal in the radial case, and more restrictive in the general one.
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Maximal Differentiability for a General Class of Quasilinear Elliptic Equations with Right-hand Side Measures
TL;DR: In this paper, the authors generalize the limiting case of Calderón-Zygmund theory for an elliptic equation with $p$-growth to the case of Orlicz growth.
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).