arXiv subjects

Panagiotis Branikas

Publications and source records attributed to Panagiotis Branikas.

2 recordsLinked to original sources

arXiv2022

Heat kernel estimates for fourth order non-uniformly elliptic operators with non strongly convex symbols

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain difficulties as it is known that, as opposed to the strongly convex case, there is no absolute exponential constant. Our estimates involve sharp constants and Finsler-type distances that are induced by the operator symbol. The main result is based on two general hypotheses, a weighted Sobolev inequalitry and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.

math.AP↗

arXiv2018

On the heat kernel of a class of fourth order operators in two dimensions: sharp Gaussian estimates and short time asymptotics

We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for operators with constant coefficients we obtain short time asymptotic estimates. The novelty of this work is that we do not assume that the associated symbol is strongly convex. The short time asymptotics reveal a behavior which is qualitatively different from that of the strongly convex case.

math.AP↗