Critical dimensions for polyharmonic operators: The Pucci-Serrin conjecture for solutions of bounded energy
Analysis of PDEs
2025-02-25 v2
Abstract
We prove a Pucci-Serrin conjecture on critical dimensions under a uniform bound on the energy. The method is based on the analysis of the Green's function of polyharmonic operators with "almost" Hardy potential.
Keywords
Cite
@article{arxiv.2407.14893,
title = {Critical dimensions for polyharmonic operators: The Pucci-Serrin conjecture for solutions of bounded energy},
author = {Frédéric Robert},
journal= {arXiv preprint arXiv:2407.14893},
year = {2025}
}
Comments
to appear in Calculus of Variations and PDEs