Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation
Yu. A. Alkhutov, Г. А. Чечкин
Abstract
An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.
Topics & Concepts
MathematicsBounded functionLipschitz continuityBoundary (topology)Mathematical analysisNeumann boundary conditionDomain (mathematical analysis)ExponentDirichlet boundary conditionPoisson's equationBoundary value problemPlane (geometry)Lipschitz domainGeometryPhilosophyLinguisticsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods