Date/heure
30 mai 2014
14:00 - 15:00
Oratrice ou orateur
Florica Cirstea
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
Let $varOmega$ be a domain in ${mathbb R}^n$ with $ngeq 2$ and $0in varOmega$. We study anisotropic elliptic equations such as $-sum_{i=1}^n,partial_{x_i} (|partial_{x_i} u|^{p_i-2}partial_{x_i} u)=delta_0$ in $varOmega$ (with Dirac mass $delta_0$ at zero), subject to $u=0$ on $partialvarOmega$. We assume that all $p_i$ are in $(1,infty)$ with their harmonic mean $p$ satisfying either Case 1: $p < n$ and $max_{1leq ileq n}{p_i}<frac{p(n-1)}{n-p}$ or Case 2: $p=n$ and $varOmega$ is bounded. We introduce a suitable notion of fundamental solution and establish its existence, together with sharp pointwise upper bound estimates near the origin for the solution and its derivatives. The latter is based on a Moser-type iteration scheme specific to each case, which is intricate due to our anisotropic analogue of the reverse H"older inequality. This is joint work with Jérôme Vétois (University of Nice)."