Advances in Differential Equations

On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner

Nataliya Vasylyeva

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Abstract

We study the nonstationary boundary-value problem for the Poisson equation in a plane corner with a dynamic boundary condition on the one part of the corner and the Dirichlet condition on the other part. We prove one-to-one solvability of the problem in weighted Hölder spaces and obtain the corresponding coercive estimates. These estimates will be useful to solve a free boundary problem.

Article information

Source
Adv. Differential Equations Volume 12, Number 10 (2007), 1167-1200.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1367241162

Mathematical Reviews number (MathSciNet)
MR2362267

Zentralblatt MATH identifier
1153.35092

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B45: A priori estimates 35C15: Integral representations of solutions 35R35: Free boundary problems

Citation

Vasylyeva, Nataliya. On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner. Adv. Differential Equations 12 (2007), no. 10, 1167--1200. https://projecteuclid.org/euclid.ade/1367241162.


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