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The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces

Please always quote using this URN:urn:nbn:de:0296-matheon-10601
  • The paper continues the study of the regularity of electronic wave functions in Hilbert spaces of mixed derivatives. It is shown that the eigenfunctions of electronic Schr\"odinger operators and their exponentially weighted counterparts possess, roughly speaking, square integrable mixed weak derivatives of fractional order $\vartheta$ for $\vartheta<3/4$. The bound $3/4$ is best possible and can neither be reached nor surpassed. Such results are important for the study of sparse grid-like expansions of the wave functions and show that their asymptotic convergence rate measured in terms of the number of ansatz functions involved does not deteriorate with the number of electrons.

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Metadaten
Author:Harry Yserentant, Hans-Christian Kreusler
URN:urn:nbn:de:0296-matheon-10601
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/13
Release Date:2012/02/13
Tag:Schrödinger equation; mixed derivatives; regularity
Institute:Technische Universität Berlin
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J10 Schrödinger operator [See also 35Pxx]
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A25 Rate of convergence, degree of approximation
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
Preprint Number:920
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