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• W2004568659 abstract "On a smooth bounded domain $$Omega subset {bf {rm R}}^N$$ we consider the Schrödinger operators − Δ − V, with V being either the critical borderline potential V(x) = (N − 2)2/4 |x|−2 or V(x) = (1/4) dist(x, ∂Ω)−2, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Schrödinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a series of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincaré. As a byproduct of our technique we are able to answer positively to a conjecture of E. B. Davies." @default.
• W2004568659 created "2016-06-24" @default.
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• W2004568659 date "2007-05-04" @default.
• W2004568659 modified "2023-10-18" @default.
• W2004568659 title "Sharp Two–Sided Heat Kernel Estimates for Critical Schrödinger Operators on Bounded Domains" @default.
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• W2004568659 doi "https://doi.org/10.1007/s00220-007-0253-z" @default.
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