Aspherical Harnack inequality for singular solutions of nonlinear elliptic equations

• Chiun-Chuan Chen ^[1] ; Chang-Shou Lin ^[2]
  1. [1] National Taiwan University

     National Taiwan University

     Taiwán

     
  2. [2] National Chung Cheng University

     National Chung Cheng University

     W. District, Taiwán

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 3-4, 2001, págs. 713-738
• Idioma: inglés
• Enlaces
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• Resumen

  • We consider a positive singular solution of where g(t) is locally bounded and positive for t > 0, r is a closed subset of B1 with vanishing Newton capacity, BR is the open ball of radius R and center 0 in R", and n > 3. By employing the method of moving planes and the localization method of R. Schoen, we prove the following inequality, where c is a positive constant and d (x) is the distance from x to r, provided that is nonincreasing in t for t large.

    This inequality is new even when u (x) is radially symmetric.