Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

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 $g(r)\ge r^q$ 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

à paraître, J. Funct. Analysis. Online http://www.sciencedirect.com.gate4.inist.fr/science/journal/aip/00221236