Noncontinuous data boundary value problems for Schrödinger equation in Lipschitz domains

Xiangxing Tao

doi:10.1007/s11464-006-0030-x

Front. Math. China ›› 2006, Vol. 1 ›› Issue (4) : 589 -603. DOI: 10.1007/s11464-006-0030-x

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Noncontinuous data boundary value problems for Schrödinger equation in Lipschitz domains

Xiangxing Tao ¹^,^a

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Abstract

The noncontinuous data boundary value problems for Schrödinger equations in Lipschitz domains and its progress are pointed out in this paper. Particularly, the L^p boundary value problems with p > 1, and H^p boundary value problems with p < 1 have been studied. Some open problems about the Besov-Sobolev and Orlicz boundary value problems are given.

Keywords

Lipschitz domain / Schrödinger equation / noncontinuous data boundary value problem / potential theory / 42B20 / 35J10

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Xiangxing Tao. Noncontinuous data boundary value problems for Schrödinger equation in Lipschitz domains. Front. Math. China, 2006, 1(4): 589-603 DOI:10.1007/s11464-006-0030-x

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