Abstract
We investigate the mixed local and nonlocal parabolic p-Laplace equation
where \(\Delta _p\) is the usual local p-Laplace operator and \(\mathcal {L}\) is the nonlocal p-Laplace type operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi–Nash–Moser iteration, we establish the local boundedness and Hölder continuity of weak solutions for such equations.
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The authors wish to thank the anonymous reviewers for many valuable comments and suggestions to improve the manuscript. This work was supported by the National Natural Science Foundation of China (No. 12071098).
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Fang, Y., Shang, B. & Zhang, C. Regularity Theory for Mixed Local and Nonlocal Parabolic p-Laplace Equations. J Geom Anal 32, 22 (2022). https://doi.org/10.1007/s12220-021-00768-0
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DOI: https://doi.org/10.1007/s12220-021-00768-0