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math.SP1998
The Hardy-Rellich Inequality for Polyharmonic Operators
Mark P. Owen
The Hardy-Rellich inequality given here generalizes a Hardy inequality of Davies (1984), from the case of the Dirichlet Laplacian of a region to that of the hig…
math.SP1998
A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators
Mark P. Owen
We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions , where the order of th…
math.SP1998
Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle
Mark P. Owen
We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasin…