A singular elliptic equation with natural growth in the gradient and a variable exponent

In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent (Formula presented.) Here Ω is an open bounded set of RR, γ(x) is a positive continuous function and f is positive function that belongs to a certain Lebesgue space....

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2015
Materias:
Nonlinear elliptic equations
Positive solutions
Singular natural growth gradient terms
Variable exponent
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v22_n6_p1935_Carmona
http://hdl.handle.net/20.500.12110/paper_10219722_v22_n6_p1935_Carmona
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10219722_v22_n6_p1935_Carmona
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spelling paper:paper_10219722_v22_n6_p1935_Carmona2023-06-08T16:00:05Z A singular elliptic equation with natural growth in the gradient and a variable exponent Rossi, Julio Daniel Nonlinear elliptic equations Positive solutions Singular natural growth gradient terms Variable exponent In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent (Formula presented.) Here Ω is an open bounded set of RR, γ(x) is a positive continuous function and f is positive function that belongs to a certain Lebesgue space. We show, among other results, that there exists a solution in the natural energy space H0 1(Ω) to this problem when γ(x) is strictly less than 2 in a strip around the boundary; while there is no solution in the energy space when there exists(Formula presented.) with (Formula presented.) such that γ(x)>2 on Γ. Moreover, since we work by approximation we can analyze the behavior of the approximated solutions un in the case in which there is no solution in H0 1(Ω). © 2015, Springer Basel. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v22_n6_p1935_Carmona http://hdl.handle.net/20.500.12110/paper_10219722_v22_n6_p1935_Carmona
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Nonlinear elliptic equations
Positive solutions
Singular natural growth gradient terms
Variable exponent
spellingShingle Nonlinear elliptic equations
Positive solutions
Singular natural growth gradient terms
Variable exponent
Rossi, Julio Daniel
A singular elliptic equation with natural growth in the gradient and a variable exponent
topic_facet Nonlinear elliptic equations
Positive solutions
Singular natural growth gradient terms
Variable exponent
description In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent (Formula presented.) Here Ω is an open bounded set of RR, γ(x) is a positive continuous function and f is positive function that belongs to a certain Lebesgue space. We show, among other results, that there exists a solution in the natural energy space H0 1(Ω) to this problem when γ(x) is strictly less than 2 in a strip around the boundary; while there is no solution in the energy space when there exists(Formula presented.) with (Formula presented.) such that γ(x)>2 on Γ. Moreover, since we work by approximation we can analyze the behavior of the approximated solutions un in the case in which there is no solution in H0 1(Ω). © 2015, Springer Basel.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title A singular elliptic equation with natural growth in the gradient and a variable exponent
title_short A singular elliptic equation with natural growth in the gradient and a variable exponent
title_full A singular elliptic equation with natural growth in the gradient and a variable exponent
title_fullStr A singular elliptic equation with natural growth in the gradient and a variable exponent
title_full_unstemmed A singular elliptic equation with natural growth in the gradient and a variable exponent
title_sort singular elliptic equation with natural growth in the gradient and a variable exponent
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v22_n6_p1935_Carmona
http://hdl.handle.net/20.500.12110/paper_10219722_v22_n6_p1935_Carmona
work_keys_str_mv AT rossijuliodaniel asingularellipticequationwithnaturalgrowthinthegradientandavariableexponent
AT rossijuliodaniel singularellipticequationwithnaturalgrowthinthegradientandavariableexponent
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