Fundamental solutions and two properties of elliptic maximal and minimal operators

Patricio L. Felmer, Alexander Quaas
2009 Transactions of the American Mathematical Society  
For a large class of nonlinear second order elliptic differential operators, we define a concept of dimension, upon which we construct a fundamental solution. This allows us to prove two properties associated to these operators, which are generalizations of properties for the Laplacian and Pucci's operators. If M denotes such an operator, the first property deals with the possibility of removing singularities of solutions to the equation where B is a ball in R N . The second property has to do
more » ... property has to do with existence or nonexistence of solutions in R N to the inequality In both cases a common critical exponent defined upon the dimension number is obtained, which plays the role of N/(N − 2) for the Laplacian.
doi:10.1090/s0002-9947-09-04566-8 fatcat:a33muysx5rfe7hu237bj2hjtwq