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On Energy Inequalities

✍ Scribed by Vesna Perišić


Book ID
102597619
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
118 KB
Volume
244
Category
Article
ISSN
0022-247X

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✦ Synopsis


We consider the Schrodinger operator H s y q q in a bounded domain

Ž . in R , d G 3, with q in the Kato class K K D and finite gauge g x s w Ž . x Ž . E exp H q X ds , where X is a Brownian motion and is the first exit time of

the Brownian motion X from the domain D. Let K and G denote the Green t ⌬ operators in D for H and , respectively. We prove that there is a positive

where f is a real, measurable function for which G f , f is finite. As a direct consequence of this double inequality, we have that the potential Gf is in the 1 Ž . 1 Ž . Sobolev space H D if and only if Kf g H D .


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