On the positivity of weak supersolutions of non-uniformly elliptic equations
Neil S. Trudinger · Bulletin of the Australian Mathematical Society · 1978
The classical maximum principle for homogeneous, second order, uniformly elliptic equations implies that non-negative, classical supersolutions are either positive or vanish identically in the interior of their domain of definition. This paper is concerned with an extension of this result to weak supersolutions of non-uniformly elliptic equations subject to only mild coefficient restrictions.