A remark on the Sobolev regularity of classical solutions of strongly elliptic equations

Research output: Contribution to journalArticle

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Abstract

We prove that C2,α (Ω̄) solutions of problem (1.2) below are in Hm+2(Ω) for all m ∈ IN, if f and the coefficients are in Hm(Ω) ∩ C0,α(Ω̄). Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11) below.

Original languageEnglish
Pages (from-to)203-219
Number of pages17
JournalMathematische Nachrichten
Volume190
DOIs
Publication statusPublished - Jan 1 1998

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Classical Solution
Elliptic Equations
Regularity
Quasilinear Equations
Coefficient

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "We prove that C2,α (Ω̄) solutions of problem (1.2) below are in Hm+2(Ω) for all m ∈ IN, if f and the coefficients are in Hm(Ω) ∩ C0,α(Ω̄). Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11) below.",
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A remark on the Sobolev regularity of classical solutions of strongly elliptic equations. / Milani, Albert.

In: Mathematische Nachrichten, Vol. 190, 01.01.1998, p. 203-219.

Research output: Contribution to journalArticle

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