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Let $C_r$ denote the open cylinder $$ C_r = \{(x,t) \in \mathbb R^{n+1} : |x| < r, -r^2 < t < 0\} $$ and consider a classical $C^{2,1}_{x,t}(C_1)$-solution to the linear heat equation $$ \...

(This is not the problem I actually care about, but an analogy with similar issues to the problem I'm actually considering.) Consider a probability space with i.i.d. random variables $X_i$ producing ...

It is well-known that the interpolation error of a cubic spline has at best order $O(h^4)$, which results from polynomials of degree $3$. Can I assume that, if one uses polynomials of degree $p$ and ...

I'm looking for a reference showing how to obtain a priori estimate for solutions to a linear second-order elliptic equation with Wentzell boundary condition in a bounded domain in $H^1$ space. The ...