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- W2047620100 abstract "In this paper, sufficient conditions are given for the coerciveness of formally positive integrodifferential forms over complex-valued functions satisfying zero boundary conditions in certain bounded domains in R2; the boundaries need not be smooth. This work extends results given by the author in Comm. Pure Appl. Math., November 1969. In addition, sufficient conditions and partial necessity conditions are given for coercive-type inequalities involving differential operators in the Holder norm; here the results hold for complexvalued functions with no boundary conditions; the regions are bounded subdomains of R. having the cone property. Introduction. In a previous paper [6] the author stated and proved two sufficient conditions for coerciveness of formally positive, constantcoefficient, homogeneous integrodifferential forms over complex-valued functions defined on sectors in the plane. The first part of this paper extends these results to the nonconstant nonhomogeneous case and certain types of bounded subdomains on R2. In the second part of this paper, some coerciveness-type results are derived for the Holder norm. I. L2-inequalities. 1.0. DEFINITIONS. If Q is a domain in R2, let C (Q) be the class of all complex-valued functions defined and continuous on Q2 and m times continuously differentiable on Q, and all of whose derivatives of order <t vanish on MQ, the boundary of Q. Let Q, be an open sector (which may be a half-plane, but not a halfline) in R2 with vertex at x0, and let Be be the open ball of radius 8 about x0. We will say that a domain Q * is of special type if it is of the form Q,) nBR Presented to the Society, April 17, 1970; received by the editors November 2, 1970. AMS 1970 subject classifications. Primary 31B45; Secondary 31A10, 31B10, 31J50." @default.
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- W2047620100 date "1972-01-01" @default.
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- W2047620100 title "Coercive inequalities for certain classes of bounded regions" @default.
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- W2047620100 doi "https://doi.org/10.1090/s0002-9939-1972-0296480-8" @default.
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