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Research Report MRR00-018
On the Weak continuity of elliptic operators and applications to potential theory
Neil S. Trudinger and Xu-Jia Wang
Abstract:
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 inequalities
for solutions.
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