Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773889 | Journal of Differential Equations | 2017 | 33 Pages |
Abstract
This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form utâdiv[A(x,t,u,âu)]=div[F] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x,t)-variables, and dependent on the solution u. Global and interior weighted W1,p(ΩT,Ï)-regularity estimates are established for weak solutions of these equations, where Ï is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for Ï=1, because of the singularity of the coefficients in (x,t)-variables.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Tuoc Phan,