Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration

2016/08/04 by Korobenko, Lyudmila, Rios, Cristian, Sawyer, Eric +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.01630

Abstract

We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form equations, and the local boundedness turns out to be sharp in more than two dimensions, answering the `Moser gap' problem left open in arXiv:1506.09203v5. Finally we obtain a maximum principle for weak solutions under the same condition on the degeneracy.

Related

• Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations
• The Moser method and boundedness of solutions to infinitely degenerate elliptic equations
• The weak maximum principle for solutions of degenerate elliptic equations with lower order terms
• The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients
• Continuity of weak solutions to rough infinitely degenerate equations