Trace estimates and invariance of the essential spectrum

Mathematics – Analysis of PDEs

Scientific paper

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To appear in Arch. Math. (Basel)

Scientific paper

We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $\R^N$ belongs to trace classes $\cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of $L^p$ norms of the difference of the coefficients. Such inequalities are useful in estimating the effect of localized perturbations of the coefficients.

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