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
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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. (2024), published online first

DOI 10.4171/JEMS/1462