Uniqueness of large solutions
Ovidiu Costin, Louis Dupaigne (LAMFA), Olivier Goubet (LAMFA)
TL;DR
This paper proves the uniqueness of large solutions for certain nonlinear PDEs in specific domains, focusing on cases with nondecreasing nonlinearities and particular geometric conditions.
Contribution
It establishes the uniqueness of large solutions in ball domains and domains with nonnegative mean curvature under asymptotic convexity of the nonlinearity.
Findings
Uniqueness of large solutions in ball domains.
Uniqueness in domains with nonnegative mean curvature.
Results applicable to asymptotically convex nonlinearities.
Abstract
Given a nondecreasing nonlinearity , we prove uniqueness of large solutions in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows