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

Albert Milani

doi:10.1002/mana.19981900111

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

Albert Milani

Mathematics & Statistical Sciences

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Abstract

We prove that C^2,α (Ω̄) solutions of problem (1.2) below are in H^m+2(Ω) for all m ∈ IN, if f and the coefficients are in H^m(Ω) ∩ C^0,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 language	English
Pages (from-to)	203-219
Number of pages	17
Journal	Mathematische Nachrichten
Volume	190
DOIs	https://doi.org/10.1002/mana.19981900111
Publication status	Published - 1998

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1002/mana.19981900111

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title = "A remark on the Sobolev regularity of classical solutions of strongly elliptic equations",

abstract = "We prove that C2,α ({\=Ω}) 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({\=Ω}). 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.",

author = "Albert Milani",

year = "1998",

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journal = "Mathematische Nachrichten",

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T1 - A remark on the Sobolev regularity of classical solutions of strongly elliptic equations

AU - Milani, Albert

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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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U2 - 10.1002/mana.19981900111

DO - 10.1002/mana.19981900111

M3 - Article

AN - SCOPUS:0005637192

SN - 0025-584X

VL - 190

SP - 203

EP - 219

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

ER -

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

Abstract

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