Regularity for solutions of non-uniformly elliptic equations in non-divergence form

  • Jongmyeong Kim

    Academia Sinica, Taipei, Taiwan
  • Se-Chan Lee

    Korea Institute for Advanced Study, Seoul, South Korea
Regularity for solutions of non-uniformly elliptic equations in non-divergence form cover
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Abstract

We prove an Aleksandrov–Bakelman–Pucci estimate for non-uniformly elliptic equations in non-divergence form. Moreover, we investigate the local behavior of solutions of such equations by proving local boundedness and a weak Harnack inequality. Here we impose an integrability assumption on ellipticity representing degeneracy or singularity, instead of specifying the particular structure of ellipticity.

Cite this article

Jongmyeong Kim, Se-Chan Lee, Regularity for solutions of non-uniformly elliptic equations in non-divergence form. Rev. Mat. Iberoam. 41 (2025), no. 6, pp. 2335–2356

DOI 10.4171/RMI/1574