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Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations (1109.2808v4)

Published 13 Sep 2011 in math.AP

Abstract: We study the boundary value problem with measures for (E1) $-\Gd u+g(|\nabla u|)=0$ in a bounded domain $\Gw$ in $\BBRN$, satisfying (E2) $ u=\gm$ on $\prt\Gw$ and prove that if $g\in L1(1,\infty;t{-(2N+1)/N}dt)$ is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When $g(r)\geq rq$ 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 $g(r)=rq$ with $1

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