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On regularity properties of a surface growth model

Published online by Cambridge University Press:  09 March 2021

Jan Burczak
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland and Mathematisches Institut, Universität Leipzig, Augustusplatz 10, D-04109Leipzig, Germany ([email protected])
Wojciech S. Ożański
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA90089, USA ([email protected])
Gregory Seregin
Affiliation:
Oxford University, UK and St Petersburg Department of Steklov Mathematical Institute, RAS, Russia ([email protected])

Abstract

We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local smoothness of solutions.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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