TY - JOUR
T1 - A remark on the Sobolev regularity of classical solutions to uniformly parabolic equations
AU - Milani, Albert
PY - 1999
Y1 - 1999
N2 - We prove that C2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace Hm+2c(Q) of Hm+2,(m+2)/2(Q) for all m ∈ IN , if f and the coefficients are in Hmc(Q) ∩ Cα,α/2 (Q̄) . We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.
AB - We prove that C2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace Hm+2c(Q) of Hm+2,(m+2)/2(Q) for all m ∈ IN , if f and the coefficients are in Hmc(Q) ∩ Cα,α/2 (Q̄) . We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.
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U2 - 10.1002/mana.19991990107
DO - 10.1002/mana.19991990107
M3 - Article
AN - SCOPUS:0040531569
SN - 0025-584X
VL - 199
SP - 115
EP - 144
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
ER -