On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner
type: Item
instance of: scholarly article
title: On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner
zbMATH Open document ID: 1153.35092
author: Nataliya V. Vasylyeva
published in: Advances in Differential Equations
publication date: 2008-09-12T00:00:00Z
review text: The author considers a non stationary boundary value problem for the Poisson equation with a dynamic boundary condition on the one part of the corner and a Dirichlet condition on the other part. The interest in this problem is because of the free boundary problem for the Laplace equation, which is the Hele--Shaw problem, in the case of free and fixed boundaries with corners at the initial time. The author follows a technique of reduction to a problem in a fixed domain. Then, differentiation leads to a non linear system of PDEs for which a one-value solvability must be achieved. Then the initial problem turns into a fixed point problem for a non linear operator. The main analytical problem is to show a weighted estimate in Hölder classes. This will be a starting point to study classical solvability of the free boundary problem related to the problem under consideration.
reviewed by: Giuseppe Di Fazio
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5343683
zbMATH Keywords: domains with corners
zbMATH Keywords: mixed boundary conditions
zbMATH Keywords: Laplace operator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5343683