Continuity of weak solutions to rough infinitely degenerate equations

2017/03/02 by Lyudmila Korobenko, Korobenko, Lyudmila, Cristian Rios +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1703.00774

openalex publication_date 2017/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a generalization of the DeGiorgi Lemma to the infinitely degenerate regime and apply it to obtain continuity of weak solutions to certain infinitely degenerate equations. This reproduces the continuity result obtained in arXiv:1506.09203 via Moser iteration, but only for homogeneous equations. However, the proofs are much less technical and more transparent.

Citations

• Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations

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