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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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Local boundedness of weak solutions of heat equations...?

I think by "standard subsolution estimate", Kurata means the following: Let $u\ge0$ be a subsolution in $Q_2:=B_2(0)\times(-4,0)$, i.e. $\partial_t u - \nabla\cdot(A\nabla u)\le 0$. Then $u$ satisfie …
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