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Pré-Publication, Document De Travail Année : 2014

Local and global properties of solutions of quasilinear Hamilton-Jacobi equations

Résumé

We study some properties of the solutions of (E) $\;-\Gd_p u+|\nabla u|^q=0$ in a domain $\Gw \sbs \BBR^N$, mostly when $p\geq q>p-1$. We give a universal priori estimate of the gradient of the solutions with respect to the distance to the boundary. We give a full classification of the isolated singularities of the positive solutions of (E), a partial classification of isolated singularities of the negative solutions. We prove a general removability result in expressed in terms of some Bessel capacity of the removable set. We extend our estimates to equations on complete non compact manifolds satisfying a lower bound estimate on the Ricci curvature, and derive some Liouville type theorems.
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Dates et versions

hal-00942304 , version 1 (05-02-2014)
hal-00942304 , version 2 (14-03-2014)
hal-00942304 , version 3 (02-07-2014)

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Marie-Françoise Bidaut-Veron, Marta Garcia-Huidobro, Laurent Veron. Local and global properties of solutions of quasilinear Hamilton-Jacobi equations. 2014. ⟨hal-00942304v3⟩
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