The Laplace Equation

DOI10.1007/978-3-319-74307-3zbMath1457.35002OpenAlexW2794509377MaRDI QIDQ4606992

Dagmar Medková

Publication date: 9 March 2018

Full work available at URL: https://doi.org/10.1007/978-3-319-74307-3

zbMATH Keywords

Dirichlet problemGreen's functioncapacityboundary value problemssuperharmonic functionsharmonic functionsNeumann problempotential methodtransmission problemsupersolutionsRobin problemvolume potentials\(L_p\)-solutionPerron-Wiener-Brelot (PWB) solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Research exposition (monographs, survey articles) pertaining to potential theory (31-02) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20) Green's functions for elliptic equations (35J08)

Related Items (19)

Classical solutions of the Dirichlet problem for the Darcy-Forchheimer-Brinkman system ⋮ Penalization method for the Navier–Stokes–Fourier system ⋮ Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions ⋮ On the Half-Space Matching Method for Real Wavenumber ⋮ On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains ⋮ A fully discrete high-order fast multiscale Galerkin method for solving boundary integral equations in a domain with corners ⋮ An inequality for the normal derivative of the Lane-Emden ground state ⋮ One Navier's problem for the Brinkman system ⋮ Transmission of harmonic functions through quasicircles on compact Riemann surfaces ⋮ Partial data inverse problems for quasilinear conductivity equations ⋮ The transmission problem on a three-dimensional wedge ⋮ On an inverse Robin spectral problem ⋮ Several non-standard problems for the stationary Stokes system ⋮ Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system ⋮ Lebesgue's criticism of Carl Neumann's method in potential theory ⋮ Weak solutions of the Robin problem for the Oseen system ⋮ A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional ⋮ The Navier-Stokes-Voigt equations with position-dependent slip boundary conditions ⋮ Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains

This page was built for publication: The Laplace Equation