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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Stability remarks to the obstacle problem for p-Laplacian type equations
TL;DR: In this article, the authors extend some convergence results for the p-obstacle problem under natural nondegeneracy conditions and without restrictions on p, and show the existence of a solution to the thermal membrane problem.
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Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation
TL;DR: In this article, the authors studied the asymptotic behavior of the solutions to the nonlinear evolution equation, where ΔpNu = Δu + (p−2) (D2u(Du/∣Du ∣)) · (Du/ ∣Du∣) is the normalized p-Laplace equation and p ≥ 2.
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A reconstruction algorithm for ultrasound-modulated diffuse optical tomography
TL;DR: In this paper, the authors developed an efficient reconstruction algorithm for ultrasound-modulated diffuse optical tomography using cross-correlations of the boundary measurements of the intensity of the light propagating in the perturbed and unperturbed medium and provided an iterative algorithm for reconstructing the optical absorption coefficient.
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Local minimizers over the Nehari manifold for a class of concave-convex problems with sign changing nonlinearity
Kaye Silva,Abiel Costa Macedo +1 more
TL;DR: In this paper, a p-Laplacian equation involving a parameter λ and a concave-convex nonlinearity containing a weight which can change sign was studied.
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(p,2)-equations asymmetric at both zero and infinity
TL;DR: In this paper, the authors considered a nonlinear nonhomogeneous elliptic equation driven by the sum of a Laplacian and a linear combination of the two with a reaction term that exhibits asymmetric behaviour.
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).