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Pré-Publication, Document De Travail Année : 2012

Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

Résumé

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
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Dates et versions

hal-00623037 , version 1 (13-09-2011)
hal-00623037 , version 2 (17-09-2011)
hal-00623037 , version 3 (17-04-2012)
hal-00623037 , version 4 (17-06-2012)

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Citer

Tai Nguyen Phuoc, Laurent Veron. Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations. 2012. ⟨hal-00623037v4⟩
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