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Pointwise estimates of solutions to the weighted porous medium equation and the fast diffusion one via weighted Riesz potentials

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Abstract

For the weighted parabolic equation v(x)ut −  div (ω(x)um − 1 ∇ u) = f(x, t), u ≥ 0, m ≠ 1, we prove the local boundedness of weak solutions in terms of the weighted Riesz potential on the right-hand side of the equation.

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  1. Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

    Yevhen Zozulia

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Correspondence to Yevhen Zozulia.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 1, pp. 116–144 January–March, 2020.

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Zozulia, Y. Pointwise estimates of solutions to the weighted porous medium equation and the fast diffusion one via weighted Riesz potentials. J Math Sci 248, 233–254 (2020). https://doi.org/10.1007/s10958-020-04872-4

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