Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions [PDF]
Anal. PDE 6 (2013) 1601-1648, 2010 We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary.
arxiv +1 more source
Semilinear elliptic systems with measure data [PDF]
, 2013 We study the Dirichlet problem for systems of the form -\Delta u^k=f^k(x,u)+\mu^k, x\in\Omega, k=1,...,n, where \Omega\subset R^d$ is an open (possibly nonregular) bounded set, \mu^1,...,\mu^n are bounded diffuse measures on \Omega, f=(f^1,...,f^n ...
Klimsiak, Tomasz
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Nonautonomous Klein–Gordon–Maxwell systems in a bounded domain
Advances in Nonlinear Analysis, 2014 This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions ...
d'Avenia Pietro +2 more
doaj +1 more source
Green functions for stationary Stokes systems with conormal derivative boundary condition in two dimensions [PDF]
arXiv, 2023 We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
arxiv
Raviart Thomas Petrov-Galerkin Finite Elements
, 2017 The general theory of Babu\v{s}ka ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard.
F Dubois +5 more
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Nonzero positive solutions of a multi-parameter elliptic system with functional BCs
, 2017 We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and covers the case of
Infante, Gennaro
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H\"older regularity for Maxwell's equations under minimal assumptions on the coefficients
, 2018 We prove global H\"older regularity for the solutions to the time-harmonic anisotropic Maxwell's equations, under the assumptions of H\"older continuous coefficients. The regularity hypotheses on the coefficients are minimal. The same estimates hold also
Alberti, Giovanni S.
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Geometrically finite Poincaré-Einstein metrics [PDF]
, 2019 We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
arxiv +1 more source
On a classical spectral optimization problem in linear elasticity
, 2014 We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space.
B Kawohl +18 more
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Two-Phase Free Boundary Problems: From Existence to Smoothness
Advanced Nonlinear Studies, 2017 We describe the theory we developed in recent times concerning two-phasefree boundary problems governed by elliptic operators with forcing terms.Our results range from existence of viscosity solutions to smoothness ofboth solutions and free boundaries ...
De Silva Daniela +2 more
doaj +1 more source