Calori Measure in Paraboli Flat Domains
نویسندگان
چکیده
Steve Hofmann1 John L. Lewis1;2 Department of Mathemati s Department of Mathemati s University of Missouri University of Kentu ky Columbia MO 65211-0001 Lexington, KY 40506-0027 email: hofmann math.missouri.edu john ms.uky.edu Kaj Nystr om2 Current Address: Department of Mathemati s Foreningssparbanken Ume a University Group Finan ial Risk Control 90187 Ume a, Sweden S-10534 Sto kholm, Sweden email: Kaj.nystrom math.umu.se kaj.nystrom foreningssparbanken.se ABSTRACT: In this paper we de ne paraboli hord ar domains and generalize a theorem of Semmes on erning quantitative approximation by graphs with small lips hitz onstants. Using this generalization we show that in a paraboli hord ar domain with vanishing onstant, the logarithm of the density of alori measure with respe t to a ertain proje tive Lebesgue measure is of vanishing mean os illation. We also obtain a partial onverse to this result. Our work generalizes to the heat equation, re ent work of Kenig and Toro for the Lapla ian. 1991 Mathemati s Subje t Classi ation. Primary 42B20, 35K05. keywords and phrases. alori measure, heat equation, absolute ontinuity, uniformly re ti able, hord ar domains.
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تاریخ انتشار 2007