Abstract
A nonnegative potential V: ℝv→ℝ is constructed for which V ∉ L q (G) for any nonempty open G⊂→v, q>0, and for which nevertheless W sup1inf2 ∩ Q(V) is dense in W sup1inf2 , i.e., is a form core for −1/2Δ in L 2.
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References
FrehseJ., ‘Capacity Methods in the Theory of Partial Differential Equations’, Jber. d. Dt. Math. Verein. 84, 1–44 (1982).
Kucherenko (Kučerenko)V. V., ‘Scattering at a Strongly Singular Potential’, Math. Notes 8, 593–599 (1970); (Transl. of Mat. Zametki 8, 217–228 (1970)).
LeinfelderH. and SimaderC. G., ‘Schrödinger Operators with Singular Magnetic Vector Potentials’, Math. Z. 176, 1–19 (1981).
SimonB., ‘Schrödinger Semigroups’, Bull. Amer. Math. Soc. (N.S.) 7, 447–526 (1982).
Voigt, J., ‘Absorption Semigroups, their Generators, and Schrödinger Semigroups’, Preprint.
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Stollmann, P., Voigt, J. A regular potential which is nowhere in L 1 . Lett Math Phys 9, 227–230 (1985). https://doi.org/10.1007/BF00402834
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DOI: https://doi.org/10.1007/BF00402834