The Poincaré problem in \(L^p\)-Sobolev spaces. I: Codimension one degeneracy

DOI10.1016/j.jfa.2004.12.006zbMath1149.35029OpenAlexW2021658876MaRDI QIDQ2577511

Dian K. Palagachev

Publication date: 22 December 2005

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2004.12.006

zbMATH Keywords

a priori estimatesPoincaré problemstrong solution\(L^p\)-Sobolev spacesuniformly elliptic operatoremergent-type vector field

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Degenerate elliptic equations (35J70) General theory of partial differential operators (47F05) A priori estimates in context of PDEs (35B45) Applications of operator theory to differential and integral equations (47N20) Weak solutions to PDEs (35D30)

Related Items (5)

A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems ⋮ \(W^{2, p}\)-a priori estimates for the emergent Poincaré problem ⋮ The Poincaré Problem inL^p-Sobolev Spaces II: Full Dimension Degeneracy ⋮ Venttsel Boundary Value Problems with Discontinuous Data ⋮ The Two-Dimensional Direct and Inverse Scattering Problems with Generalized Oblique Derivative Boundary Condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The oblique derivative problem. I
• Regularity estimates for the oblique derivative problem
• A global solution to a two-dimensional Riemann problem involving shocks as free boundaries
• Regularity estimates for the oblique derivative problem on non-smooth domains. I
• Pseudo-differential operators and non-elliptic boundary problems
• On the diffraction of Poincaré waves
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• The tangential oblique derivative problem for nonlinear elliptic equations
• A boundary value problem with an oblique derivative
• ON THE THEORY OF SOLVABILITY OF A PROBLEM WITH OBLIQUE DERIVATIVE
• The tangential oblique derivative problem for second order quasilinear parabolic operators
• Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem
• Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients
• -Solvability for the Parabolic Poincaré Problem
• THE OBLIQUE DERIVATIVE PROBLEM
• ON A DEGENERATING PROBLEM WITH DIRECTIONAL DERIVATIVE
• A singular boundary value problem for uniformly elliptic operators

This page was built for publication: The Poincaré problem in \(L^p\)-Sobolev spaces. I: Codimension one degeneracy