arXiv subjects

Longyu Wu

Publications and source records attributed to Longyu Wu.

2 recordsLinked to original sources

arXiv2025

Limiting behavior of inertial manifolds for stochastic differential equations driven by non-Gaussian Levy noise

In this paper, we study the limiting behavior for stochastic differential equations driven by non-Gaussian alpha-stable Levy noise as alpha approaches 2. We first prove the convergence of solutions for system driven by alpha-stable Levy noise to those of the system driven by Brownian motion. Then we construct the C^1 inertial manifolds for both systems and show that these inertial manifolds converge in probability as alpha rightarrow2.

math.DS↗

arXiv2024

The $L_q$ Minkowski problem for $\mathbf{p}$-harmonic measure

In this paper, we consider an extremal problem associated with the solution to a boundary value problem. Our main focus is on establishing a variational formula for a functional related to the $\mathbf{p}$-harmonic measure, from which a new measure is derived. This further motivates us to study the Minkowski problem for this new measure. As a main result, we prove the existence of solutions to the $L_q$ Minkowski problem associated with the $\mathbf{p}$-harmonic measure for $0<q<1$ and $1<\mathbf{p}\ne n+1$.

math.AP↗