Premium
A Remark on the Sobolev Regularity of Classical Solutions to Uniformly Parabolic Equations
Author(s) -
Milani Albert
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19991990107
Subject(s) - mathematics , sobolev space , subspace topology , pure mathematics , mathematical analysis , sobolev inequality
We prove that C 2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace H c m+2 ( Q ) of H m+2,(m+2)/2(Q) for all m ∈ ℕ, if f and the coefficients are in H c m ( Q )∪ C α,α/2 (Q̄). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.