On the second-order regularity of solutions to the parabolic p-Laplace equation
Feng, Y., Parviainen, M., & Sarsa, S. (2022). On the second-order regularity of solutions to the parabolic p-Laplace equation. Journal of Evolution Equations, 22, Article 6. https://doi.org/10.1007/s00028-022-00760-3
Published inJournal of Evolution Equations
DisciplineAnalyysin ja dynamiikan tutkimuksen huippuyksikköMatematiikkaAnalysis and Dynamics Research (Centre of Excellence)Mathematics
© 2022 Crown
In this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that D(|Du|p−2+s2Du) exists as a function and belongs to L2loc with s>−1 and 1
<∞. The range of s is sharp.
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Additional information about fundingYawen Feng was supported by China Scholarship Council, No. 202006020186. Saara Sarsa was supported by the Academy of Finland, the Centre of Excellence in Analysis and Dynamics Research and the Academy of Finland, Project 308759.
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