Nonnegative solutions of some quasilinear elliptic inequalities and applications
Lorenzo D'Ambrosio, Enzo Mitidieri

TL;DR
This paper establishes conditions under which weak solutions to certain quasilinear elliptic inequalities are nonnegative, extending results to subelliptic operators on Carnot groups.
Contribution
It provides new criteria ensuring nonnegativity of solutions for a class of quasilinear elliptic inequalities, including extensions to subelliptic operators on Carnot groups.
Findings
Weak solutions are nonnegative under specified conditions.
Extensions to subelliptic operators on Carnot groups.
Applicable to a broad class of quasilinear inequalities.
Abstract
Let be a continuous function. We prove that under some additional assumptions on and , weak solutions of the differential inequality on are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot Groups are considered.
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