On the regularity theory for mixed local and nonlocal quasilinear elliptic equations
By P. Garain, Juha Kinnunen. 2021
127 citations recorded by the source corpus.
Abstract. We consider mixed local and nonlocal quasilinear parabolic equations of p-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions, local Hölder continuity of weak solutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the pointwise behavior of the semicontinuous representatives. Our main results are valid for sign changing solutions. Our approach is purely analytic and is based on energy estimates and the De Giorgi theory.
View Paper: https://www.semanticscholar.org/paper/0a78415dcfa4ff5554b8568f12aa341e473f4807
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- P. Garain
- Erik Lindgren
- Lorenzo Brasco
- Cristiana De Filippis
- Giampiero Palatucci
- Stefano Biagi
- Janne Korvenpää
Citations in the corpus
- Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, result): “In the nonlinear setting p 6= 2, for f = 0, regularity results of weak solutions in terms of local boundedness, Harnack estimates, local Hölder continuity and semicontinuity results have been obtained in Garain-Kinnunen [28].”