Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle

By S. Armstrong, Boyan Sirakov. 2010

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We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of ℝ n . The simplicity and robustness of our maximum principle-based argument provides for its applicability to many elliptic inequalities and systems, including quasilinear operators such as the p-Laplacian, and nondivergence form fully nonlinear operators such as Bellman-Isaacs operators. Our method gives new and optimal results in terms of the nonlinear functions appearing in the inequalities, and applies to inequalities holding in the whole space as well as exterior domains and cone-like domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f74595f87e1af44f53fb103e36ad4e0ed33db64a

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

A natural constraint approach to normalized solutions of nonlinear Schr\"odinger equations and systems (2016, background): “cerned, using again Lemma 3.11 we note that for any k, µ2 >0 Ψk(x) = λ2|x|2 +µ2c2 3k 2 +|x|2c(x) and h(k) = ( +∞ if λ2 >0 µ2c2 3k 2 if λ 2 = 0, so that (f3) holds. In conclusion, Theorem 4.1 in [4] is applicable, and together with the strong maximum principle implies that ¯u2 ≡ 0. Conclusion o”