A priori bounds for solutions of a wide class of quasilinear degenerate elliptic inequalities are proved. As an outcome we deduce sharp Liouville theorems. Our investigation includes inequalities associated to p-Laplacian and the mean curvature operators in Carnot groups setting. No hypotheses on the solutions at infinity are assumed. General results on the sign of solutions for quasilinear coercive/noncoercive inequalities are considered. Related applications to population biology and chemical reaction theory are also studied. © 2009 Elsevier Inc.
D’Ambrosio, L., & Mitidieri, E. (2010). A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities. Advances in Mathematics, 224(3), 967–1020. https://doi.org/10.1016/j.aim.2009.12.017