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arXiv · 1412.4613

Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations

Marie-Françoise Bidaut-Véron·Marta Garcia-Huidobro·Laurent Véron
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Abstract

We study the boundary behaviour of the solutions of (E) $-\Delta_p u+|\nabla u|^q=0$ in a domain $\Omega \subset \mathbb{R}^N$, when $N\geq p > q >p-1$. We show the existence of a critical exponent $q_* < p$ such that if $p-1 < q < q_*$ there exist positive solutions of (E) with an isolated singularity on $\partial\Omega$ and that these solutions belong to two different classes of singular solutions. If $q_*\leq q < p$ no such solution exists and actually any boundary isolated singularity of a positive solution of (E) is removable. We prove that all the singular positive solutions are classified according the two types of singular solutions that we have constructed.

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron. 2014-12-15. Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations. https://arxiv.org/abs/1412.4613

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