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Ultracontractivity of heat semigroups with non-local Robin boundary conditions via two-sided bounds for a positive eigenfunction
We study heat semigroups on bounded Lipschitz domains $Ω\subset \mathbb{R}^{d}$ with dimension $d>2$ under non-local Robin boundary conditions. The boundary operator $B \in \mathcal{L}( \mathrm{L}^{2}(\partialΩ))$ is allowed to destroy the positivity of the semigroup. We assume that there exists a p
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