Results 91 to 100 of about 376,175 (295)
Convexity of solutions of semilinear elliptic equations
Duke Mathematical Journal, 1985 On considere le probleme elliptique suivant Δu=f(u) dans Ω, u=M sur ∂Ω ou Ω est un domaine convexe de R 2 et M est soit une constante reelle soit +∞. On etablit que, pour une bonne fonction monotone g(t), pout toute solution u on a g(u) est strictement convexe dans ...
Caffarelli, Luis A., Friedman, Avner
openaire +3 more sources
Multiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature
Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 2081-2137, March 2024.Abstract We address the one‐parameter minmax construction for the Allen–Cahn energy that has recently lead to a new proof of the existence of a closed minimal hypersurface in an arbitrary compact Riemannian manifold Nn+1$N^{n+1}$ with n≥2$n\ge 2$ (Guaraco's work, relying on works by Hutchinson, Tonegawa, and Wickramasekera when sending the Allen–Cahn ...
Costante Bellettini
wiley +1 more source
Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 3-36, January 2024.Abstract We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well‐known that: ‐For n=2$n=2$, there exist Morse index 1 solutions whose L∞$L^\infty$ norm goes to infinity. ‐For n≥3$n \ge 3$, uniform boundedness holds in the subcritical case for power‐type nonlinearities, while for ...
Alessio Figalli, Yi Ru‐Ya Zhang
wiley +1 more source
Electronic Journal of Differential Equations, 2016 In this article, we study a class of semilinear elliptic equations involving Hardy-Sobolev critical exponents and Hardy-Sobolev-Maz'ya potential in a bounded domain. We obtain the existence of positive solutions using the Mountain Pass Lemma.
Rui-Ting Jiang, Chun-Lei Tang
doaj
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In this work, we deal with a fourth‐order parabolic equation with variable exponent logarithmic nonlinearity. We obtain the global existence and blowup solutions using the energy functional and potential well method.
Gülistan Butakın +3 more
wiley +1 more source
Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms [PDF]
arXiv, 2011 In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always converge.
arxiv
Semilinear fractional elliptic equations involving measures
Journal of Differential Equations, 2014 We study the existence of weak solutions of (E) $ (- )^ u+g(u)= $ in a bounded regular domain $ $ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus $, where $(- )^ $ denotes the fractional Laplacian with $ \in(0,1)$, $ $ is a Radon measure and $g$ is a nondecreasing function satisfying some extra hypothesis.
Laurent Veron, Huyuan Chen, Huyuan Chen
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Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems
Electronic Journal of Differential Equations, 1999 When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj
Elliptic Equations Involving Meausres [PDF]
Stationary Partial Differential equations, Volume 1, M. Chipot, P.
Quittner (Ed.) (2004) 593-712, 2008 We present the moste recent results dealing with the theory of semilinear elliptic equations with measures ...
arxiv
Inverse problems for fractional semilinear elliptic equations [PDF]
Nonlinear Analysis, 2020 Ru-Yu Lai, Yi-Hsuan Lin
semanticscholar +1 more source