On the weak continuity of elliptic operators and applications to potential theory

Neil S. Trudinger, Xu-Jia Wang
2002 American Journal of Mathematics  
In this paper, we establish weak continuity results for quasilinear elliptic and subelliptic operators of divergence form, acting on corresponding classes of subharmonic functions. These results are analogous to our earlier results for fully nonlinear k-Hessian operators. From the weak continuity, we derive various potential theoretic results including capacity estimates, potential estimates and the Wiener criterion for regular boundary points. Our methods make substantial use of Harnack
more » ... e of Harnack inequalities for solutions. Running title: Weak continuity of elliptic operators
doi:10.1353/ajm.2002.0012 fatcat:jm2hut5dzjbvbi6vxhqrq66axq