\(L^{1,p}\)-coercitivity and estimates of the Green function of the Neumann problem in a convex domain

DOI10.1007/s10958-014-1656-yzbMath1302.35146OpenAlexW2002982460MaRDI QIDQ467565

Yury A. Alkhutov, Vladimir Gilelevich Maz'ya

Publication date: 3 November 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-1656-y

zbMATH Keywords

eigenvaluePoisson equationGreen functionNeumann problemNeumann-Laplace operator

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) Green's functions for elliptic equations (35J08)

Related Items (6)

Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions ⋮ Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones ⋮ PMA celebrates the 85th birthday of V. G. Maz'ya ⋮ Energy stability for a class of semilinear elliptic problems ⋮ Elliptic equations in convex domains ⋮ Characterization of isoperimetric sets inside almost-convex cones

Cites Work

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• Spectral stability of the Neumann Laplacian.
• Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations
• Uniqueness theorems on conformal deformation of metrics, sobolev inequalities, and an eigenvalue estimate
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• On Harnack's theorem for elliptic differential equations

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