Yuval Peres

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math.AP2026

Homogenization for the $p$ -Laplacian in a $d$ -dimensional ball perforated along the unit sphere: the critical case $p = d$

Peter V. Gordon, Yuval Peres

We study a boundary value problem for the $p$ -Laplacian in the perforated domain $B (0, I ¨ ) ∖ I^ \subset R^{d}$ , where $I ¨ > 1$ and $I^$ is the union of many small compact…

math.AP2026

Explosion versus decay for boundary derivatives of $p$ -harmonic functions as $p$ tends to 1: nonlocality

Yuval Peres, Han Wang

We consider the Dirichlet problem for the $p$ -Laplacian on a bounded Lipschitz domain $I^c ◯ \subset R^{d}$ with a ${0, 1}$ -valued function as the boundary condition and study…

Homogenization for the p-Laplacian in a d-dimensional ball perforated along the unit sphere: the critical case p=d

Explosion versus decay for boundary derivatives of p-harmonic functions as p tends to 1: nonlocality

Homogenization for the $p$ -Laplacian in a $d$ -dimensional ball perforated along the unit sphere: the critical case $p = d$

Explosion versus decay for boundary derivatives of $p$ -harmonic functions as $p$ tends to 1: nonlocality