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We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel way Moser t
Externí odkaz:
http://arxiv.org/abs/2405.06304
We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a number of a
Externí odkaz:
http://arxiv.org/abs/2402.03098
In this paper we study double obstacle problems involving $(p,q)-$Laplace type operators. In particular, we analyze the asymptotics of the solutions on fractal and pre-fractal boundary domains.
Externí odkaz:
http://arxiv.org/abs/2312.16574
Autor:
Beznea, Lucian, Teodor, Alexandra
We give a probabilistic representation of the solution to a semilinear elliptic Dirichlet problem with general (discontinuous) boundary data. The boundary behaviour of the solution is in the sense of the controlled convergence initiated by A. Cornea.
Externí odkaz:
http://arxiv.org/abs/2312.00126
We construct using variational methods Hamiltonian Stationary Surfaces with Isolated Schoen-Wolfson Conical Singularities. We obtain these surfaces through a convergence process reminiscent to the Ginzburg-Landau asymptotic analysis in the strongly r
Externí odkaz:
http://arxiv.org/abs/2311.15734
Autor:
Barkatou, Mohammed
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some classical
Externí odkaz:
http://arxiv.org/abs/2304.04107
Publikováno v:
Adv. Nonlinear Stud. 23 (2023), no.1, Paper No. 20220078, 14 pp
In this paper, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a spe
Externí odkaz:
http://arxiv.org/abs/2304.01726
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 7183-7219 (2024)
This article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,
Externí odkaz:
https://doaj.org/article/a9c9c780a50547ddaac0878ff6b41be8
Autor:
Umezu, Kenichiro
We study the positive solutions of the logistic elliptic equation with a nonlinear Neumann boundary condition that models coastal fishery harvesting ([18]). An essential role is played by the smallest eigenvalue of the Dirichlet eigenvalue problem, w
Externí odkaz:
http://arxiv.org/abs/2301.12147
We extend some theorems for the Infinity-Ground State and for the Infinity-Potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent explicit solution disproves a conjecture
Externí odkaz:
http://arxiv.org/abs/2301.09022