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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todo:paper_10219722_v22_n6_p1935_Carmona2023-10-03T15:56:43Z A singular elliptic equation with natural growth in the gradient and a variable exponent Carmona, J. Martínez-Aparicio, P.J. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 |
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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 Carmona, J. Martínez-Aparicio, P.J. Rossi, J.D. 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. |
| format |
JOUR |
| author |
Carmona, J. Martínez-Aparicio, P.J. Rossi, J.D. |
| author_facet |
Carmona, J. Martínez-Aparicio, P.J. Rossi, J.D. |
| author_sort |
Carmona, J. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10219722_v22_n6_p1935_Carmona |
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