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hal-00623037, version 4

Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

Tai Nguyen Phuoc () 1, Laurent Veron () 1

Abstract: We study the boundary value problem with measures for (E1) $-\Gd u+g(|\nabla u|)=0$ in a bounded domain $\Gw$ in $\BBR^N$, satisfying (E2) $ u=\gm$ on $\prt\Gw$ and prove that if $g\in L^1(1,\infty;t^{-(2N+1)/N}dt)$ is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When $g(r)\geq r^q$ 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

  • 1:  Laboratoire de Mathématiques et Physique Théorique (LMPT)
  • CNRS : UMR6083 – Université François Rabelais - Tours
  • Domain : Mathematics/Analysis of PDEs
  • Keywords : quasilinear elliptic equations – isolated singularities – Borel measures – Bessel capacities
  • Comment : Journal of Functional Analysis 263 (2012) 1487-1538
  • Available versions :  v1 (2011-09-13) v2 (2011-09-18) v3 (2012-04-17) v4 (2012-06-17)
 
  • hal-00623037, version 4
  • http://hal.archives-ouvertes.fr/hal-00623037
  • oai:hal.archives-ouvertes.fr:hal-00623037
  • From: Laurent Veron <>
  • Submitted on: Sunday, 17 June 2012 09:47:49
  • Updated on: Tuesday, 28 August 2012 16:28:37