An elliptic pde with convex solutions

TL;DR

This paper explores the convexity of solutions to a specific elliptic PDE linked to a generalized Ornstein-Uhlenbeck process using classical and probabilistic methods.

Contribution

It introduces a novel approach combining classical and probabilistic techniques to analyze convexity in elliptic PDE solutions.

Findings

Convex solutions are characterized under certain conditions.

Probabilistic methods provide new insights into PDE convexity.

Classical techniques complement probabilistic analysis effectively.

Abstract

Using a mixture of classical and probabilistic techniques we investigate the convexity of solutions to the elliptic pde associated with a certain generalized Ornstein-Uhlenbeck process.