Publikace na Matematicko-fyzikální fakulta |
2014
Abstrakt
We consider energy solutions of the inhomogeneous parabolic p-Laplacien system \partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g. We show in the case p\geq 2 that if the right hand side g is locally in L^\infty(\text{BMO}), then u is locally in L^\infty(\mathcal{C}^1), where \mathcal{C}^1 is the 1-H\"older--Zygmund space.
This is the borderline case of the Calder\'on-Zygmund theorey. We provide local quantitative estimates.
We also show that finer properties of g are conserved by D u, e.g.\ H\"older continuity. Moreover, we prove a new decay for gradients of p-caloric solutions for all \frac{2n}{n+2}<p<\infty.