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
Citations
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Journal ArticleDOI
P-capacity vs surface-area ☆
TL;DR: In this article, it was shown that if Ω ⊂ R n is a convex, compact, smooth set with its interior Ω ∘ ≠ ∅ and the mean curvature H ( ∂ Ω, ⋅ ) > 0 of its boundary ∂Ω, then ( n ( p − 1 ) p ( n − 1) p (n − 1 n − p ) 1 − p σ n− 1 ≤ ( ∫ ∂ ǫ (H ( ∀ ∀, Ⓟ ) )
Journal ArticleDOI
The Concavity of the Gaussian Curvature of the Convex Level Sets of \(p\) -Harmonic Functions with Respect to the Height
Xi-Nan Ma,Wei Zhang +1 more
TL;DR: In this paper, an auxiliary function which comes from the combination of the norm of gradient of the function and the Gaussian curvature of the level sets of a convex function was proposed.
Posted Content
Convexity of level sets for elliptic problems in convex domains or convex rings: two counterexamples
TL;DR: In this paper, it was shown that the superlevel sets of the solutions do not inherit the convexity or ring-convexity of the domain, and two counterexamples to this quasiconcavity property were given for some two-dimensional convex domains and for some convex rings in any dimension.
Journal ArticleDOI
Hopf's lemma for a class of singular/degenerate PDE-S
TL;DR: In this paper, the boundary point lemma in certain C-1,C-Dini-type domains was investigated for a class of singular/degenerate PDEs, including p-Laplacian.
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.