On a regularity theorem for weak solutions to transmission problems with internallipschitz boundaries

L. Escauriaza; E. B. Fabes; G. Verchota

doi:10.1090/S0002-9939-1992-1092919-1

On a regularity theorem for weak solutions to transmission problems with internallipschitz boundaries

L. Escauriaza, E. B. Fabes, G. Verchota

Department of Mathematics

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

90 Scopus citations

Abstract

We show that if u is a weak solution to div(AVu) = 0 on an open set Ω containing a Lipschitz domain D, where Then, the nontangential maximal function of the gradient of u lies in L2(dD).

Original language	English (US)
Pages (from-to)	1069-1076
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	115
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1992-1092919-1
State	Published - Aug 1992

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "On a regularity theorem for weak solutions to transmission problems with internallipschitz boundaries",

abstract = "We show that if u is a weak solution to div(AVu) = 0 on an open set Ω containing a Lipschitz domain D, where Then, the nontangential maximal function of the gradient of u lies in L2(dD).",

author = "L. Escauriaza and Fabes, {E. B.} and G. Verchota",

year = "1992",

month = aug,

doi = "10.1090/S0002-9939-1992-1092919-1",

language = "English (US)",

volume = "115",

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journal = "Proceedings of the American Mathematical Society",

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T1 - On a regularity theorem for weak solutions to transmission problems with internallipschitz boundaries

AU - Escauriaza, L.

AU - Fabes, E. B.

AU - Verchota, G.

PY - 1992/8

Y1 - 1992/8

N2 - We show that if u is a weak solution to div(AVu) = 0 on an open set Ω containing a Lipschitz domain D, where Then, the nontangential maximal function of the gradient of u lies in L2(dD).

AB - We show that if u is a weak solution to div(AVu) = 0 on an open set Ω containing a Lipschitz domain D, where Then, the nontangential maximal function of the gradient of u lies in L2(dD).

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U2 - 10.1090/S0002-9939-1992-1092919-1

DO - 10.1090/S0002-9939-1992-1092919-1

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VL - 115

SP - 1069

EP - 1076

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

On a regularity theorem for weak solutions to transmission problems with internallipschitz boundaries

Abstract

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