Artículo Original
Sobre la existencia de cotas a priori para soluciones positivas de problemas elípticos, II
Publicado 2019-02-19
Palabras clave
- Estimaciones a priori,
- no-linealidades subcríticas,
- método de “moving planes”,
- igualdad de Pohozaev,
- hipérbola crítica de Sobolev
- bifurcación biparamétrica ...Más
Cómo citar
Pardo, R. (2019). Sobre la existencia de cotas a priori para soluciones positivas de problemas elípticos, II. Revista Integración, Temas De matemáticas, 37(1), 113–148. https://doi.org/10.18273/revint.v37n1-2019006
Resumen
Continuamos estudiando la existencia de cotas uniformes a priori para soluciones positivas de equaciones elípticas subcríticas
(P)p − \Delta_pu = f(u), en \Omega, u = 0, sobre ∂\Omega,
Proporcionamos condiciones suficientes para que las soluciones positivas en C1,μ (\overline{\Omega }) de una clase de problemas elípticos subcríticos tengan cotas a-priori L∞ en dominios acotados, convexos, y de clase C2. En esta parte II, extendemos nuestros resultados a sistemas elípticos Hamiltonianos −\Delta u = f(v), −\Delta v = g(u), en \Omega , u = v = 0 sobre ∂ \Omega, cuando f(v) = vp/[ln(e + v)]α, g(u) = uq/[ln(e + u)]β, con α, β > 2/(N − 2), y p, q varían sobre la hipérbola crítica de Sobolev 1/p+1 + 1/q+1 = N−2/N . Para ecuaciones elípticas cuasilineales que involucran al operador p-Laplacian, existen cotas a-priori para soluciones positivas de (P)p en el espacio C1,μ(\overline {\Omega }), μ ∈ (0, 1), cuando f(u) = up⋆−1/[ln(e + u)]α, con p∗ = Np/(N − p), y α > p/(N − p). También estudiamos el comportamiento asintótico de soluciones radialmente simétric uα = uα(r) de (P)2 cuando α → 0.
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Referencias
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