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Mathematics > Analysis of PDEs

arXiv:2201.09560 (math)
[Submitted on 24 Jan 2022 (v1), last revised 1 Jul 2022 (this version, v2)]

Title:Trace and boundary singularities of positive solutions of a class of quasilinear equations

Authors:Marie-Françoise Bidaut-Véron (IDP), Laurent Véron (IDP)
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Abstract:We study properties of positive functions satisfying (E) --$\Delta$u+m|$\nabla$u| q -- u p = 0 is a domain $\Omega$ or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for the existence of a solution to (E) with a nonnegative measure $\mu$ as boundary data, and these conditions are expressed in terms of Bessel capacities on the boundary. We also study removable boundary singularities and solutions with an isolated singularity on $\partial$$\Omega$. The different results depends on two critical exponents for p = p c := N +1 N --1 and for q = q c := N +1 N and on the position of q with respect to 2p p+1. Contents
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:2201.09560 [math.AP]
  (or arXiv:2201.09560v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2201.09560
Journal reference: Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, In press

Submission history

From: Laurent Veron [view email] [via CCSD proxy]
[v1] Mon, 24 Jan 2022 10:02:34 UTC (27 KB)
[v2] Fri, 1 Jul 2022 12:00:24 UTC (28 KB)
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