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local higher integrability

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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On regularity properties of a surface growth model
Part of
Jan Burczak, Wojciech S. Ożański, Gregory Seregin
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 6 / December 2021

Published online by Cambridge University Press:

09 March 2021, pp. 1869-1892

Print publication:

December 2021
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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.