On the existence of a priori bounds for positive solutions of elliptic problems, II

  1. Pardo, Rosa 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Integración: Temas de matemáticas

ISSN: 0120-419X

Año de publicación: 2019

Título del ejemplar: Revista Integración, temas de matemáticas

Volumen: 37

Número: 1

Páginas: 113-148

Tipo: Artículo

DOI: 10.18273/REVINT.V37N1-2019006 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Integración: Temas de matemáticas

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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