Journal of Fixed Point Theory and Applications

, Volume 5, Issue 2, pp 353-395

First online:

Some remarks on singular solutions of nonlinear elliptic equations. I

  • Luis CaffarelliAffiliated withDepartment of Mathematics, The University of Texas
  • , Yan Yan LiAffiliated withDepartment of Mathematics, Rutgers University Email author 
  • , Louis NirenbergAffiliated withCourant Institute

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We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes.

Mathematics Subject Classification (2000).

35J69 58J05 53C21 35J60


Nonlinear elliptic equations strong maximum principle method of moving planes singular solutions