Algebraic and geometric topology. Proceedings of symposia in by James R. Milgram

By James R. Milgram

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On [~x 0. x’~, y~. (4) (iii) [HSlder regularity in the second variable] For x ~ l~ and t ~ I, y ~ Kt(x, y) is a HSlder continuous function in ~ and there exist constants ce > 0 and p > 0 such that C2 DEFINITION1 We say that L has the Gaussian property (G) (resp. (G~oc)) the Kt(x, y) satisfies (i,ii,iii) for I = (0, ~) (resp. I = (0, T) fbr some REMARK 2 Recall that a HSlder continuous function on a set E extends to its closure. Thus, if L has the property (G) or (G~oc) then Kt(x,y) C~’(gt x f~) fo t ~ I, which shows that this definition includes interior and boundaryregularity.

Widman. The Green function for uniformly elliptic equations. , 37:303-342, 1982. 14. P. Kenig and J. Pipher. The Neumannproblem for elliptic equations with non-smooth coefficients. Inventiones Matematicae, 113:447-509, 1993. 32 Auscher and Tchamitchiam 15. T. H°°-functional calculus of elliptic partial differential operators in LO-spaces. PhDthesis, Mathematics, Physics, Computing and Electronics at Macquarie university, 1990. 16. G. A. A. Plamenevskii. Absence of De Giorgitype theorelns for strongly elliptic equations with complex coefficients.

It was shown shown by, G. Lumer and F. Neubrander [12] that any function that is analytic in a postsectorial region and satisfies a certain growth condition is in the asymptotic Laplace transform of a. continuous function. Suppose a meromorphic function on such a region multiplied by the asymptotic Laplace transfor~n of a regularizer yields an analytic function satisfying the growth conditions. Then, this meromorphicfunction is an element of the asymptotic Laplace transform of a generalized function.

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