A remark on the Sobolev regularity of classical solutions to uniformly parabolic equations

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove that C2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace Hm+2 c(Q) of Hm+2,(m+2)/2(Q) for all m ∈ IN , if f and the coefficients are in Hm c(Q) ∩ Cα,α/2 (Q̄) . We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.

Original languageEnglish
Pages (from-to)115-144
Number of pages30
JournalMathematische Nachrichten
Volume199
DOIs
Publication statusPublished - Jan 1 1999

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Quasilinear Problems
Classical Solution
Global Existence
Parabolic Equation
Regularity
Subspace
Coefficient

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "We prove that C2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace Hm+2 c(Q) of Hm+2,(m+2)/2(Q) for all m ∈ IN , if f and the coefficients are in Hm c(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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A remark on the Sobolev regularity of classical solutions to uniformly parabolic equations. / Milani, Albert.

In: Mathematische Nachrichten, Vol. 199, 01.01.1999, p. 115-144.

Research output: Contribution to journalArticle

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AB - We prove that C2+α,1+α/2 (Q̄) solutions of problem (1.6) below are in a subspace Hm+2 c(Q) of Hm+2,(m+2)/2(Q) for all m ∈ IN , if f and the coefficients are in Hm c(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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