Non-classical solutions of the -Laplace equation

  • Maria Colombo

    EPFL, Lausanne, Switzerland
  • Riccardo Tione

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Non-classical solutions of the $p$-Laplace equation cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

In this paper we settle Iwaniec and Sbordone’s 1994 conjecture concerning very weak solutions to the -Laplace equation. Namely, on the one hand we show that distributional solutions of the -Laplace equation in for and are classical weak solutions if their weak derivatives belong to certain cones. On the other hand, we construct via convex integration non-energetic distributional solutions if this cone condition is not met, thus disproving Iwaniec and Sbordone’s conjecture in general.

Cite this article

Maria Colombo, Riccardo Tione, Non-classical solutions of the -Laplace equation. J. Eur. Math. Soc. 27 (2025), no. 12, pp. 4845–4890

DOI 10.4171/JEMS/1462