W01,1 -solutions for elliptic problems having gradient quadratic lower order terms
In this paper we deal with solutions of problems of the type (Formula presented). where 0 < α ≤ a(x) ≤ β, {pipe}b(x){pipe} ≤ γ, γ > 0, f ∈ L2 (Ω) and Ω is a bounded subset of ℝN with N ≥ 3. We prove the existence of at least one solution for such a problem in the space W01,1 (Ω) ∩ L2 (Ω) if th...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/24460 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/24460 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas Nonlinear elliptic equations W 1,1 0 (Ω) solutions Quadratic gradient terms |
| Sumario: | In this paper we deal with solutions of problems of the type (Formula presented). where 0 < α ≤ a(x) ≤ β, {pipe}b(x){pipe} ≤ γ, γ > 0, f ∈ L2 (Ω) and Ω is a bounded subset of ℝN with N ≥ 3. We prove the existence of at least one solution for such a problem in the space W01,1 (Ω) ∩ L2 (Ω) if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: (Formula presented). where in this case a(x) ≡ b(x) = α > 0. |
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