A new \(H^2\) regularity condition of the solution to Dirichlet problem of the Poisson equation and its applications

DOI10.1007/s10114-019-8015-3zbMath1430.35042OpenAlexW2999157960WikidataQ126387388 ScholiaQ126387388MaRDI QIDQ2287774

Ming-Jun Lai, Fuchang Gao

Publication date: 21 January 2020

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-019-8015-3

zbMATH Keywords

non-divergence formuniformly positive reach

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Strong solutions to PDEs (35D35)

Related Items

Trivariate spline collocation methods for numerical solution to 3D Monge-Ampère equation ⋮ A Multivariate Spline Based Collocation Method for Numerical Solution of Partial Differential Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary value problems for the Laplacian in convex and semiconvex domains
• A bivariate spline method for second order elliptic equations in non-divergence form
• Metric entropy of classes of sets with positive reach
• Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems
• Sopra una classe di equazioni ellittiche a coefficienti misurabili
• Sulle equazioni ellittiche del secondo ordine di tipo non variazionale a coefficienti discontinui
• Linear and quasilinear elliptic equations
• On the existence of certain singular integrals
• Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
• Curvature Measures
• On the Vector Sum of Two Convex Sets in Space
• Bivariate Splines of Various Degrees for Numerical Solution of Partial Differential Equations
• Spline Functions on Triangulations
• $L^2$-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
• A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form
• Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
• SHARP REGULARITY COEFFICIENT ESTIMATES FOR COMPLEX-VALUED ACOUSTIC AND ELASTIC HELMHOLTZ EQUATIONS
• Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients