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
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Isolated singularities of positive solutions of elliptic equations with weighted gradient term
TL;DR: In this paper, the authors studied the behavior near 0 of positive solutions of equation (E) − Δu + |x|αup +|x|β|∇u|q = 0 in Ω ∖{0, where α > −2, β > −1, p > 1, and q > 1.
Journal ArticleDOI
Least energy nodal solutions for elliptic equations with indefinite nonlinearity
TL;DR: In this paper, the authors proved the existence of a nodal solution with two nodal domains for the Dirichlet problem with indefinite nonlinearity Dpu = ljuj p 2 u + f(x)juj g 2 u in a bounded domain W R n, provided l 2 ( ¥,l 1 ), where l 1 is a critical spectral value.
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A quasilinear problem with fast growing gradient
Hamilton Bueno,Grey Ercole +1 more
TL;DR: It is proved that there exists a region D in the λ β -plane where the Dirichlet problem has at least one positive solution.
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A Free Boundary Problem for a Fluid Flow in a Heterogeneous Porous Medium.
TL;DR: In this paper, the authors studied the problem of seepage of a fluid through a porous medium, assuming the flow governed by a nonlinear Darcy law and nonlinear leaky boundary conditions.
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.
Journal ArticleDOI
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).