On regularity of the extremal solution of the Dirichlet problem for some semilinear elliptic equations of the second order

• Autores: S. Eidelman, Y. Eidelman
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 3, 2005, págs. 957-960
• Idioma: inglés
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• Resumen

  • We consider the problem on the regularity of the extremal positive solution of the Dirichlet problem for superlinear elliptic equations with a positive parameter. We prove the smoothness of the extremal solution for a certain class of nonlinearities. In this class we distinguish a subclass of functions for which the extremal solution is classical in the space of any dimension