Quasilinear and Hessian type equations with exponential reaction and measure data

Nguyen Quoc, Hung ; Veron, Laurent

HAL, hal-00823874 / Harvested from HAL

Résumé

We prove existence results concerning equations of the type $-\Gd_pu=P(u)+\gm$ for $p>1$ and $F_k[-u]=P(u)+\gm$ with $1\leq k<\frac{N}{2}$ in a bounded domain $\Omega$ or the whole $\mathbb{R}^N$, where $\gm$ is a positive Radon measure and $P(u)\sim e^{au^\beta}$ with $a>0$ and $\beta\geq 1$. Sufficient conditions for existence are expressed in terms of the fractional maximal potential of $\gm$. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of $\gm$. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence results for a general Wolff potential equation under the form $u={\bf W}_{\alpha,p}^R[P(u)]+f$ in $\mathbb{R}^N$, where $0

Détail

Publié le : 2014-05-09
Classification:  quasilinear elliptic equations,  Hessian equations,  Wolff potential,  maximal functions,  Borel measures,  Orlicz capacities,  31C15, 32 F10, 35J92, 35R06, 46E30,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]