Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations

摘要

We study the boundary value problem with measures for (E1) -δu+g(|?;u|)=0 in a bounded domain Ω in RN, satisfying (E2) u=μ on ?Ω and prove that if g∈L ~1(1, ∞;t ~(-(2N+1)/N)dt) 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