A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities
By L. D’Ambrosio, Enzo Mitidieri. 2010
135 citations recorded by the source corpus.
Abstract 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7f1bd84c59da153a1f4d31c9cb68fb3ba0f238bf
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Computational Theory and Mathematics
- S. Armstrong
- Alberto Farina
- J. Serrin
- Boyan Sirakov
- Jean-Christophe Mourrat
- Zhongwei Shen
- Berardino Sciunzi
- Tuomo Kuusi
In Mathematical Physics
Citations in the corpus
- Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds (2015, unknown): “, [2], [19], [18], [21], [22], [3]) and on Riemannian manifolds (see [11], [12], [14] [16], [17], [27], [28]).”
- Entire solutions of completely coercive quasilinear elliptic equations, II (2011, background): “Other important and closely related work corresponding to Examples 1 and 2 is due to Mitidieri and Pohozaev [10] (see also [15],[5],[6],[7],[9],[11]); all of these works are, however, restricted to positive (or non-negative) solutions u.”
- Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle (2010, result): “A notable exception is the very recent work of D’Ambrosio and Mitidieri [19], who obtained various nonexistence results for divergence-form quasilinear inequalities in the whole space with only a local hypothesis on the function f s near s = 0, as in (1.”