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

Albert Milani

doi:10.1002/mana.19991990107

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

Albert Milani

Mathematics & Statistical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	115-144
Number of pages	30
Journal	Mathematische Nachrichten
Volume	199
DOIs	https://doi.org/10.1002/mana.19991990107
Publication status	Published - 1999

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1002/mana.19991990107

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@article{e01466cd6750411dba3480b27bf8e70b,

title = "A remark on the Sobolev regularity of classical solutions to uniformly parabolic equations",

abstract = "We prove that C2+α,1+α/2 ({\=Q}) 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 ({\=Q}) . We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.",

author = "Albert Milani",

year = "1999",

doi = "10.1002/mana.19991990107",

language = "English",

volume = "199",

pages = "115--144",

journal = "Mathematische Nachrichten",

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publisher = "Wiley-VCH Verlag",

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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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UR - https://www.scopus.com/pages/publications/0040531569#tab=citedBy

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 -

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

Abstract

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