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• W2413843573 abstract "We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation $partial_t u +(-Delta)^s u=0$, $0<s<1$, posed in the whole space $mathbb{R}^N$ with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative data and solutions, which is given in one direction by the representation formula, in the other one by the initial trace. We review many of the typical properties of the solutions, in particular we prove optimal pointwise estimates and new Harnack inequalities." @default.
• W2413843573 created "2016-06-24" @default.
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• W2413843573 date "2016-06-02" @default.
• W2413843573 modified "2023-09-27" @default.
• W2413843573 title "Optimal Existence and Uniqueness Theory for the Fractional Heat Equation" @default.
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• W2413843573 hasPublicationYear "2016" @default.
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