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- W2267332173 abstract "SUMMARY. We consider the gauge function G for the Neumann problem for J4-f g in the half space D ? {(a, x) 6 Rd : a > 0}, where q is independent of a and is periodic in X. It is shown that if G j? oo, then G is a bounded continuous function on Cl(D). If H(x) = 00 J G(<x, x)d<z # oo, it is shown that the corresponding Feynman-Kac semi-group decays 0 exponentially. The gauge function plays a central role in studying the Neumann problem for the Schr?dinger operator, &+q, in a bounded domain. The gauge func tion for th3 Neumann problem is defined in terms of the reflected Brownian motion. If the gauge function is not identically infinite, then the so called gauge theorem states that it is a bounded continuous function and that the corresponding Feynman-Kac semigroup exponentially decays ; (and in such a case the existence of a unique solution to the Neumann problem is guaran teed). A crucial ingredient of the proof of the gauge theorem is that the transition probability density function of the reflected Brownian motion in a bounded region is bounded away from zero ; see Chung and Hsu [2], Chung" @default.
- W2267332173 created "2016-06-24" @default.
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- W2267332173 date "1994-01-01" @default.
- W2267332173 modified "2023-09-27" @default.
- W2267332173 title "On the gauge for the Neumann problem in the half space" @default.
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