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1 vote

Heat Equation on $[0,T] \times \mathbb{R}^n$

See Linear and quasilinear equations of parabolic type, 1968, by O.A. Ladyzenskaja, V.A. Solonnikov, and N.N. Ural'ceva, Theorem 6.1 in Chapter III. See also Theorem 9.1, Chapter IV, in the same book, …
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Schauder regularity heat equation

For a partial answer, see Theorem 6.48 in Second order parabolic differential equations, 1996, by Gary Lieberman. There is an additional assumption that $f$ belongs to the Morrey space $M^{1,n+1+\alp …
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