Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or, equivalently, the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The ?rst line consists of existence and regularity results. Usually the solution exists and "gains two orders of differen- ation" with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under...
Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order station...