[{"command":"settings","settings":{"basePath":"\/educacion\/","pathPrefix":"","ajaxPageState":{"theme":"fa_facned","theme_token":"_bFQbNLsvG1hKOnIPGZNT1JdKqOQTOeeIh1oXvXZ3K8"}},"merge":true},{"command":"informationProductos","data":{"html":"\u003Cdiv class=\u0022entity entity-productos productos-productos clearfix\u0022\u003E\n\n      \u003Ch2\u003E\n              Existencia, unicidad y H^2-regularidad interior de un problema semilineal.           \u003C\/h2\u003E\n  \n  \u003Cdiv class=\u0022content\u0022\u003E\n    \u003Cdiv class=\u0022form-item form-type-item\u0022\u003E\n  \u003Clabel\u003Efecha de publicaci\u00f3n \u003C\/label\u003E\n 2008-06-30\n\u003C\/div\u003E\n\u003Cdiv class=\u0022form-item form-type-item\u0022\u003E\n  \u003Clabel\u003ETipo de producto acad\u00e9mico \u003C\/label\u003E\n Publicaciones de investigaci\u00f3n\n\u003C\/div\u003E\n\u003Cdiv class=\u0022form-item form-type-item\u0022\u003E\n  \u003Clabel\u003EAutor(es) \u003C\/label\u003E\n Gerardo Arturo Loaiza Motato, Jairo Duque \n\u003C\/div\u003E\n\u003Cdiv class=\u0022form-item form-type-item\u0022\u003E\n  \u003Clabel\u003EDescripcion \u003C\/label\u003E\n In this paper we prove the existence and uniqueness of the weak solution of the semiliear \r\nproblem, defined in a bounded domain \u03a9 \u2282 RN with smooth boundary and f \u2208 L^2 (\u03a9). In our problem we assume a Dirichlet boundary condition. With appropriated hypothesis on the nonlinear term F and linear operator we prove the existence of a unique u \u2208 H_0^1 (\u03a9) that satisfies the weak formulation of (P). The proof is based on nonlinear Lax\u2013Milgram\u2019s theorem. Finally we can prove, under additional hypotheses, that the weak solution is locally H^2.\n\u003C\/div\u003E\n\u003Cdiv class=\u0022form-item form-type-item\u0022\u003E\n  \u003Clabel\u003EDescarga \u003C\/label\u003E\n \n\u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n"}}]