Extending the well-known connection between classical linear potential theory and
probability theory (through the interplay between harmonic functions and martingales) to the …

We present new quantitative estimates for the radially symmetric configuration concerning
Serrin's overdetermined problem for the torsional rigidity, Alexandrov's Soap Bubble …

Mean value formulas are of great importance in the theory of partial differential equations:
many very useful results are drawn, for instance, from the well-known equivalence between …

Functions of Least Gradient Page 1 Monographs in Mathematics 110 Wojciech Górny José M.
Mazón Functions of Least Gradient Page 2 Page 3 Monographs in Mathematics Volume 110 …

We prove a new asymptotic mean value formula for the p-Laplace operator, Δ _pu= div (| ∇
u|^ p-2 ∇ u),\quad 1< p< ∞ Δ pu= div (|∇ u| p-2∇ u), 1< p<∞ valid in the viscosity sense. In …

We start providing a quantitative stability theorem for the rigidity of an overdetermined
problem involving harmonic functions in a punctured domain. Our approach is inspired by …

In this paper we find viscosity solutions to an elliptic system governed by two different
operators (the Laplacian and the infinity Laplacian) using a probabilistic approach. We …

We prove uniform convergence in Lipschitz domains of approximations to p-harmonic
functions obtained using the natural p-means introduced by Ishiwata, Magnanini, and …

We prove a lower bound on the sharp Poincaré–Sobolev embedding constants for general
open sets, in terms of their inradius. We consider the following two situations: planar sets …

In a recent paper, the last three authors showed that a game-theoretic p-harmonic function v
is characterized by an asymptotic mean value property with respect to a kind of mean value …