Abstract
We prove that if u is a locally Lipschitz continuous function on an open set \(\mathcal {X} \subset \mathbb {R}^{n+1}\) satisfying the nonlinear heat equation \(\partial _t u = \Delta (|u|^{p-1} u)\), \(p > 1\), weakly away from the zero set \(u^{-1} (0)\) in \(\mathcal {X}\), then u is a weak solution to this equation in all of \(\mathcal {X}\).
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Acknowledgements
The first author gratefully acknowledges the financial support of the grant of the Russian Federation Government for scientific research under the supervision of leading scientist at the Siberian Federal University, Contract No. 14.Y26.31.0006.
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This paper is dedicated to Lev Aizenberg on the occasion of his 80th birthday.
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Fedchenko, D., Tarkhanov, N. A Radó theorem for the porous medium equation. Bol. Soc. Mat. Mex. 24, 427–437 (2018). https://doi.org/10.1007/s40590-017-0169-3
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DOI: https://doi.org/10.1007/s40590-017-0169-3