Geometric inequalities via a general comparison principle for interacting gases

Geometric inequalities via a general comparison principle for interacting gases

A Terminal Comparison Principle for Differential Inequalities

A General Conformal Geometric Reflection Principle

We prove a generalization of the Schwarz–Carathéodory reflection principle for analytic maps f from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric λ(w) |dw|. This yields a necessary and sufficient condition for f to have an analytic continuation in terms of the pullback of the metric λ(w) |dw| under the map f .

A Liouville comparison principle for solutions of quasilinear differential inequalities

This work is devoted to the study of a Liouville comparison principle for entire weak solutions of quasilinear differential inequalities of the form A(u) + |u|q−1u ≤ A(v) + |v|q−1v on Rn, where n ≥ 1, q > 0, and the operator A(w) belongs to a class of the so-called α-monotone operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1 < p ≤ 2. The re...

Auxiliary Principle Technique for Extended General Variational Inequalities

In this paper, we use the auxiliary principle technique to study the existence of a solution of the extended general variational inequalities, which were introduced and studied by the author. Several special cases are also discussed.