Affiliation:
1. Institute for Advanced Study in Mathematics Harbin Institute of Technology Harbin PR China
2. School of Mathematics Harbin Institute of Technology Harbin PR China
Abstract
AbstractWe consider the mixed local and nonlocal functionals with nonstandard growth
with , , and being a bounded domain. We study, utilizing expansion of positivity, local behavior of the minimizers of such problems, involving local boundedness, local Hölder continuity, and Harnack inequality. This solves a problem raised by De Filippis and Mingione [Math. Ann. 388 (2024) 262–328].
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Fundamental Research Funds for the Central Universities