KFU. Card publication. Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents

KAZAN
FEDERAL UNIVERSITY

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ENTROPY AND RENORMALIZED SOLUTIONS OF ANISOTROPIC ELLIPTIC EQUATIONS WITH VARIABLE NONLINEARITY EXPONENTS

Form of presentation

Articles in international journals and collections

Year of publication

2019

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Authors, employees of KFU

Kozhevnikova Larisa Mikhaylovna, author

Bibliographic description in the original language

Kozhevnikova L. M., Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents//SBORNIK MATHEMATICS. - 2019. - Vol.210, Is.3. - P.417-446.

Annotation

The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in $L_1$. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration.

Keywords

anisotropic elliptic equation, entropy solution, renormalized solution, existence of a solution, variable exponent, Dirichlet problem.

The name of the journal

Sbornik Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=203126&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Kozhevnikova Larisa Mikhaylovna	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Kozhevnikova L. M., Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents//SBORNIK MATHEMATICS. - 2019. - Vol.210, Is.3. - P.417-446.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=203126&p_lang=2	ru_RU
dc.description.abstract	Sbornik Mathematics	ru_RU
dc.description.abstract	The Dirichlet problem is considered in arbitrary domains for a class of second-order anisotropic elliptic equations with variable nonlinearity exponents and right-hand sides in $L_1$. It is proved that an entropy solution exists in anisotropic Sobolev spaces with variable exponent. It is proved that the entropy solution obtained is a renormalized solution of the problem under consideration.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	anisotropic elliptic equation	ru_RU
dc.subject	entropy solution	ru_RU
dc.subject	renormalized solution	ru_RU
dc.subject	existence of a solution	ru_RU
dc.subject	variable exponent	ru_RU
dc.subject	Dirichlet problem.	ru_RU
dc.title	Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents	ru_RU
dc.type	Articles in international journals and collections	ru_RU