$L^p$ solvability of the Stationary Stokes problem on domains with conical singularity in any dimension [PDF]
arXiv, 2010 The Dirichlet boundary value problem for the Stokes operator with $L^p$ data in any dimension on domains with conical singularity (not necessary a Lipschitz graph) is considered. We establish the solvability of the problem for all $p\in (2-\varepsilon,\infty]$ and also its solvability in $C(\overline{D})$ for the data in $C(\partial D)$
Dindoš, Martin, Maz'ya, Vladimir
arxiv +5 more sources
On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains [PDF]
, 2020 We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz ...
Coscia, Vincenzo
core +1 more source
On the existence and multiplicity of topologically twisting incompressible $H$-harmonic maps and a structural H-condition [PDF]
, 2020 No description ...
Morrison, George, Taheri, Ali
core +1 more source
A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian [PDF]
, 2015 We prove that the unique solution to the Dirichlet problem with constant source term for the inhomogeneous normalized infinity Laplacian on a convex domain of $\mathbb{R}^N$ is of class $C^1$. The result is obtained by showing as an intermediate step the
Crasta, Graziano, Fragalà, Ilaria
core +2 more sources
A stationary free boundary problem modeling electrostatic MEMS [PDF]
, 2011 A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values.
Christoph Walker +11 more
core +3 more sources
An Efficient Method For Solving Highly Anisotropic Elliptic Equations [PDF]
, 2011 Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterised by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest derivative in ...
Alberto Scotti +19 more
core +3 more sources
Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs
Advanced Nonlinear Studies, 2020 We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities.
Biagi Stefano +2 more
doaj +1 more source
Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains [PDF]
, 2014 We provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations.
Infante, Gennaro, Pietramala, Paolamaria
core +1 more source
Elliptic regularity theory applied to time harmonic anisotropic Maxwell's equations with less than Lipschitz complex coefficients [PDF]
, 2014 The focus of this paper is the study of the regularity properties of the time harmonic Maxwell's equations with anisotropic complex coefficients, in a bounded domain with $C^{1,1}$ boundary. We assume that at least one of the material parameters is $W^{1,
Alberti, Giovanni S., Capdeboscq, Yves
core +2 more sources
Multiple solutions to quasi-linear elliptic Robin systems [PDF]
arXiv, 2022 Two opposite constant-sign solutions to a non-variational p-Laplacian system with Robin boundary conditions are obtained via sub-super-solution techniques. A third nontrivial one comes out by means of topological degree arguments.
arxiv