On the solvability of a transmission problem for the Laplace operator with a dynamic boundary condition on a nonregular interface

DOI10.1016/j.jmaa.2012.03.023zbMath1248.35066OpenAlexW2076732180MaRDI QIDQ432424

Nataliya Vasylyeva, Borys V. Bazaliy

Publication date: 4 July 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.03.023

zbMATH Keywords

Laplace operatortransmission problemweighted Hölder spacesnonsmooth domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• The Muskat problem with surface tension and a nonregular initial interface
• A degenerate diffusion problem with dynamical boundary conditions
• The transmission problem in domains with a corner point for the Laplace operator in weighted Hölder spaces
• A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions
• On the solvability of some nonclassical boundary-value problem for the Laplace equation in the plane corner
• Nonlinear elliptic systems with dynamic boundary conditions
• Régularité de la solution d'un problème de transmission
• Global classical solution of Muskat free boundary problem.
• On the linear theory of gravity waves: the theorem of existence and uniqueness
• The Hele-Shaw problem with surface tension in a half-plane
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• Estimates in 𝐿_{𝑝} and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
• Boundary-value problems for partial differential equations in non-smooth domains
• Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
• Classical Solutions of Multidimensional Hele--Shaw Models
• Well-posedness of two-phase Hele–Shaw flow without surface tension
• On one proof of the classical solvability of the Hele-Shaw problem with free boundary
• ON THE LAPLACE EQUATION WITH NON-LINEAR DYNAMICAL BOUNDARY CONDITIONS
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