A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations

2020/11/24 by Scott, James M., Mengesha, Tadele
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.12779

Abstract

In this note we prove an estimate on the level sets of a function with (p, q) growth that depends on the difference quotient of a bounded weak solution to a nonlocal double phase equation. This estimate is related to a self improving property of these solutions.

Related

• Self-improving Inequalities for bounded weak solutions to nonlocal double phase equations
• Regularity results for a class of nonlocal double phase equations with VMO coefficients
• Gradient regularity for nonlocal double phase equations
• Bounded minimizers of double phase problems at nearly linear growth
• Hölder regularity results for parabolic nonlocal double phase problems