Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

2011/09/13 by Tai Nguyen Phuoc, Phuoc, Tai Nguyen, Veron, Laurent · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1109.2808

openalex publication_date 2011/09/13 · openalex created_date 2022/02/25 · openalex updated_date 2026/07/28

Abstract

We study the boundary value problem with measures for (E1) -\Gd u+g(|∇ u|)=0 in a bounded domain \Gw in \BBR^N, satisfying (E2) u=\gm on \prt\Gw and prove that if g∈ L¹(1,∞;t^-(2N+1)/Ndt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r)≥ r^q with q>1 we prove that any positive function satisfying (E1) admits a boundary trace which is an outer regular Borel measure, not necessarily bounded. When g(r)=r^q with 1

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