Modifications of the gehring lemma appearing in the study of parabolic initial-boundary-value problems

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Modifications of the gehring lemma appearing in the study of parabolic initial-boundary-value problems. / Arkhipova, A. A.

In: Journal of Mathematical Sciences, Vol. 97, No. 4, 01.01.1999, p. 4189-4205.

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

BibTeX

@article{43cab871555d4cb68bd813ebdfba8819,

title = "Modifications of the gehring lemma appearing in the study of parabolic initial-boundary-value problems",

abstract = "Some modifications of the Gehring lemma are required in the study of solutions to parabolic initial-boundary-value problems, The Gehring lemma assert that if a function satisfies the reverse H{\"o}lder-inequalities in a cube, then the integrability degree of this function in Q increases in this cube. Earlier, the author formulated some generalizations of the Gehring lemma and used them in the study of parabolic quasilinear systems with controlled nonlinearity orders. In this paper, the proof of these generalizations are given. On the basis of the modification of the Gehring lemma proposed by the author, the theorem on the reverse H{\"o}lder inequalities is formulated in a form convenient for obtaining Lp-estimates for the derivatives of solutions to parabolic problems. An application of this theorem is also demonstrated. Bibliography: 19 titles.",

author = "Arkhipova, {A. A.}",

year = "1999",

month = jan,

day = "1",

doi = "10.1007/BF02365039",

language = "English",

volume = "97",

pages = "4189--4205",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Modifications of the gehring lemma appearing in the study of parabolic initial-boundary-value problems

AU - Arkhipova, A. A.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Some modifications of the Gehring lemma are required in the study of solutions to parabolic initial-boundary-value problems, The Gehring lemma assert that if a function satisfies the reverse Hölder-inequalities in a cube, then the integrability degree of this function in Q increases in this cube. Earlier, the author formulated some generalizations of the Gehring lemma and used them in the study of parabolic quasilinear systems with controlled nonlinearity orders. In this paper, the proof of these generalizations are given. On the basis of the modification of the Gehring lemma proposed by the author, the theorem on the reverse Hölder inequalities is formulated in a form convenient for obtaining Lp-estimates for the derivatives of solutions to parabolic problems. An application of this theorem is also demonstrated. Bibliography: 19 titles.

AB - Some modifications of the Gehring lemma are required in the study of solutions to parabolic initial-boundary-value problems, The Gehring lemma assert that if a function satisfies the reverse Hölder-inequalities in a cube, then the integrability degree of this function in Q increases in this cube. Earlier, the author formulated some generalizations of the Gehring lemma and used them in the study of parabolic quasilinear systems with controlled nonlinearity orders. In this paper, the proof of these generalizations are given. On the basis of the modification of the Gehring lemma proposed by the author, the theorem on the reverse Hölder inequalities is formulated in a form convenient for obtaining Lp-estimates for the derivatives of solutions to parabolic problems. An application of this theorem is also demonstrated. Bibliography: 19 titles.

UR - http://www.scopus.com/inward/record.url?scp=53149138167&partnerID=8YFLogxK

U2 - 10.1007/BF02365039

DO - 10.1007/BF02365039

M3 - Article

AN - SCOPUS:53149138167

VL - 97

SP - 4189

EP - 4205

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 15546831