Journal ArticleDOI
Capacitary functions in convex rings
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1977-09-01. It has received 203 citations till now.read more
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Correctors and Field Fluctuations for the $p_{\epsilon}(x)$-Laplacian with Rough Exponents
Silvia Jimenez,Robert Lipton +1 more
TL;DR: In this paper, a corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided. But the correctors are used to develop bounds on the local singularity strength for gradient fields inside micro-structured media.
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On a Bernoulli-type overdetermined free boundary problem.
TL;DR: In this paper, the authors study a Bernoulli-type free boundary problem and generalize the work of Henrot and Shahgholian to quasi-linear elliptic PDEs.
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Correctors and Field Fluctuations for the $p_{\epsilon}(x)$-Laplacian with Rough Exponents: Cases$1<p_1\leq p_2\leq 2$ and $1<p_1\leq 2\leq p_2$
TL;DR: In this article, a corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided, and the correctors are used to develop bounds on the local singularity strength for gradient fields inside micro-structured media.
Concavity properties for quasilinear equations and optimality remarks
TL;DR: In this paper , the authors studied quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schrodinger equations of the type $$-{\rm div}\big(a(u)
abla u\big) + \frac{a'(u),}{2} |
abbla u|^2 = f(u)'s \quad \hbox{in $\Omega$', where ''Omega'' is a convex bounded domain of ''mathbb{R}^N''.
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Weak Harnack inequalities for eigenvalues and a constant rank theorem for level sets
Bianlian Yan,Ping Guang Zhang +1 more
TL;DR: In this article , convex level sets of solutions of a class of quasilinear elliptic equations were considered and a weak Harnack inequality for the eigenvalues of the Weingarten tensor of level sets was obtained.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.