7 papers
A simplified characterization of stable-like heat kernel estimates
Mathav Murugan
We study heat kernel estimates for symmetric pure jump processes on general metric measure spaces. Building on recent progress in the local setting due to S.~Eriksson-Bique, we dev…
Uniqueness of the maximal solution of the supercooled Stefan problem in 1D
Kai Hong Chau, Young-Heon Kim, Mathav Murugan
We prove uniqueness of the maximal weak solutions to the supercooled Stefan problem in 1 dimension. This follows by showing that in 1 dimension, the optimal solution of the corresp…
Diffusions and random walks with prescribed sub-Gaussian heat kernel estimates
Mathav Murugan
Given suitable functions , we obtain necessary and sufficient conditions on for the existence of a metric measure space and a symmetric diff…
On the energy image density conjecture of Bouleau and Hirsch
Sylvester Eriksson-Bique, Mathav Murugan
We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). Beyond the original framework of Dirichlet structures, we establish the energy image dens…
Martingale and analytic dimensions coincide under Gaussian heat kernel bounds
Mathav Murugan
Given a strongly local Dirichlet form on a metric measure space that satisfies Gaussian heat kernel bounds, we show that the martingale dimension of the associated diffusion proces…
First-order Sobolev spaces, self-similar energies and energy measures on the SierpiÅski carpet
Mathav Murugan, Ryosuke Shimizu
We construct and investigate -Sobolev space, -energy, and the corresponding -energy measures on the planar SierpiÅski carpet for all . Our method…