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A geometric estimate for a periodic Schrödinger operator

100%

Friedrich T.

Colloquium Mathematicum

2000

tom 83

nr 2

209-216

We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator $-4{d^2}/{ds^2} + κ^2(s)$ with potential given by the curvature of a closed curve.

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Generalization of p-regularity notion and tangent cone description in the singular case

86%

Grzegorczyk W., Medak B., Tret’yakov A. A.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2012

tom 66

nr 2

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Colloquium Mathematicum

1 Friedrich T.

1 Grzegorczyk W.

1 Medak B.

1 Tret’yakov A. A.

1 2012

1 2000

Wyniki wyszukiwania

A geometric estimate for a periodic Schrödinger operator

Generalization of p-regularity notion and tangent cone description in the singular case