<title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent
Estudiamos la existencia y unicidad de soluciones y entropía debil para el problema no lineal inhomogeneos de Neumann con valores de frontera que involucra el <img border=0 width=54 height=28 id="_x0000_i1053" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción:...
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2012-01-01
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| Series: | Cubo |
| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000200002 |
| _version_ | 1818235495112507392 |
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| author | Stanislas Ouaro |
| author_facet | Stanislas Ouaro |
| author_sort | Stanislas Ouaro |
| collection | DOAJ |
| description | Estudiamos la existencia y unicidad de soluciones y entropía debil para el problema no lineal inhomogeneos de Neumann con valores de frontera que involucra el <img border=0 width=54 height=28 id="_x0000_i1053" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace de la forma<img border=0 width=582 height=24 id="_x0000_i1052" src="http:/fbpe/img/cubo/v14n2/art02-01.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-01.jpg"> en Omega,<img border=0 width=160 height=22 id="_x0000_i1051" src="http:/fbpe/img/cubo/v14n2/art02-09.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-09.jpg"> sobre <img border=0 width=36 height=27 id="_x0000_i1050" src="http:/fbpe/img/cubo/v14n2/art02-10.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-10.jpg">, donde Omega es en un dominio abierto suave y acotado en <img border=0 width=228 height=29 id="_x0000_i1049" src="http:/fbpe/img/cubo/v14n2/art02-02.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-02.jpg">para <img border=0 width=71 height=25 id="_x0000_i1048" src="http:/fbpe/img/cubo/v14n2/art02-11.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-11.jpg">. Probamos la existencia y unicidad de una solución débil para <img border=0 width=155 height=36 id="_x0000_i1047" src="http:/fbpe/img/cubo/v14n2/art02-05.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-05.jpg">, la existencia y unicidad de una solución de entropía para<img border=0 width=42 height=29 id="_x0000_i1046" src="http:/fbpe/img/cubo/v14n2/art02-07.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-07.jpg">data f y ö independiente de u y la existencia de soluciones debiles para f dependiente sobre <img border=0 width=179 height=36 id="_x0000_i1045" src="http:/fbpe/img/cubo/v14n2/art02-12.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-12.jpg">.<br>We study the existence and uniqueness of weak and entropy solutions for the nonlinear inhomogeneous Neumann boundary value problem involving the <img border=0 width=54 height=28 id="_x0000_i1062" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace of the form -<img border=0 width=582 height=24 id="_x0000_i1061" src="http:/fbpe/img/cubo/v14n2/art02-01.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-01.jpg"> where <img border=0 width=27 height=28 id="_x0000_i1060" src="http:/fbpe/img/cubo/v14n2/art02-08.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-08.jpg">is a smooth bounded open domain in <img border=0 width=228 height=29 id="_x0000_i1059" src="http:/fbpe/img/cubo/v14n2/art02-02.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-02.jpg">. We prove the existence and uniqueness of a weak solution for data <img border=0 width=219 height=25 id="_x0000_i1058" src="http:/fbpe/img/cubo/v14n2/art02-03.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-03.jpg">, the existence and <img border=0 width=165 height=32 id="_x0000_i1057" src="http:/fbpe/img/cubo/v14n2/art02-04.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-04.jpg">uniqueness of an entropy solution for <img border=0 width=42 height=29 id="_x0000_i1056" src="http:/fbpe/img/cubo/v14n2/art02-07.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-07.jpg">data f and ö independent of u and the existence of weak solutions for f dependent on u and <img border=0 width=155 height=36 id="_x0000_i1055" src="http:/fbpe/img/cubo/v14n2/art02-05.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-05.jpg">. |
| first_indexed | 2024-12-12T11:54:52Z |
| format | Article |
| id | doaj.art-b1923bc3bf3f4fdf8b28373ebbb489f6 |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-12-12T11:54:52Z |
| publishDate | 2012-01-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-b1923bc3bf3f4fdf8b28373ebbb489f62022-12-22T00:25:14ZengUniversidad de La FronteraCubo0716-77760719-06462012-01-011421541<title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponentStanislas OuaroEstudiamos la existencia y unicidad de soluciones y entropía debil para el problema no lineal inhomogeneos de Neumann con valores de frontera que involucra el <img border=0 width=54 height=28 id="_x0000_i1053" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace de la forma<img border=0 width=582 height=24 id="_x0000_i1052" src="http:/fbpe/img/cubo/v14n2/art02-01.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-01.jpg"> en Omega,<img border=0 width=160 height=22 id="_x0000_i1051" src="http:/fbpe/img/cubo/v14n2/art02-09.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-09.jpg"> sobre <img border=0 width=36 height=27 id="_x0000_i1050" src="http:/fbpe/img/cubo/v14n2/art02-10.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-10.jpg">, donde Omega es en un dominio abierto suave y acotado en <img border=0 width=228 height=29 id="_x0000_i1049" src="http:/fbpe/img/cubo/v14n2/art02-02.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-02.jpg">para <img border=0 width=71 height=25 id="_x0000_i1048" src="http:/fbpe/img/cubo/v14n2/art02-11.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-11.jpg">. Probamos la existencia y unicidad de una solución débil para <img border=0 width=155 height=36 id="_x0000_i1047" src="http:/fbpe/img/cubo/v14n2/art02-05.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-05.jpg">, la existencia y unicidad de una solución de entropía para<img border=0 width=42 height=29 id="_x0000_i1046" src="http:/fbpe/img/cubo/v14n2/art02-07.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-07.jpg">data f y ö independiente de u y la existencia de soluciones debiles para f dependiente sobre <img border=0 width=179 height=36 id="_x0000_i1045" src="http:/fbpe/img/cubo/v14n2/art02-12.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-12.jpg">.<br>We study the existence and uniqueness of weak and entropy solutions for the nonlinear inhomogeneous Neumann boundary value problem involving the <img border=0 width=54 height=28 id="_x0000_i1062" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace of the form -<img border=0 width=582 height=24 id="_x0000_i1061" src="http:/fbpe/img/cubo/v14n2/art02-01.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-01.jpg"> where <img border=0 width=27 height=28 id="_x0000_i1060" src="http:/fbpe/img/cubo/v14n2/art02-08.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-08.jpg">is a smooth bounded open domain in <img border=0 width=228 height=29 id="_x0000_i1059" src="http:/fbpe/img/cubo/v14n2/art02-02.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-02.jpg">. We prove the existence and uniqueness of a weak solution for data <img border=0 width=219 height=25 id="_x0000_i1058" src="http:/fbpe/img/cubo/v14n2/art02-03.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-03.jpg">, the existence and <img border=0 width=165 height=32 id="_x0000_i1057" src="http:/fbpe/img/cubo/v14n2/art02-04.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-04.jpg">uniqueness of an entropy solution for <img border=0 width=42 height=29 id="_x0000_i1056" src="http:/fbpe/img/cubo/v14n2/art02-07.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-07.jpg">data f and ö independent of u and the existence of weak solutions for f dependent on u and <img border=0 width=155 height=36 id="_x0000_i1055" src="http:/fbpe/img/cubo/v14n2/art02-05.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-05.jpg">.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000200002Generalized Lebesgue and Sobolev spacesWeak solutionEntropy solution<img border=0 width=54 height=28 id="_x0000_i1054" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace operator |
| spellingShingle | Stanislas Ouaro <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent Cubo Generalized Lebesgue and Sobolev spaces Weak solution Entropy solution <img border=0 width=54 height=28 id="_x0000_i1054" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace operator |
| title | <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent |
| title_full | <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent |
| title_fullStr | <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent |
| title_full_unstemmed | <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent |
| title_short | <title language="eng">Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent |
| title_sort | title language eng weak and entropy solutions for a class of nonlinear inhomogeneous neumann boundary value problem with variable exponent |
| topic | Generalized Lebesgue and Sobolev spaces Weak solution Entropy solution <img border=0 width=54 height=28 id="_x0000_i1054" src="http:/fbpe/img/cubo/v14n2/art02-06.jpg" alt="Descripción: http:/fbpe/img/cubo/v14n2/art02-06.jpg">Laplace operator |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000200002 |
| work_keys_str_mv | AT stanislasouaro titlelanguageengweakandentropysolutionsforaclassofnonlinearinhomogeneousneumannboundaryvalueproblemwithvariableexponent |