Coercive inequalities for certain classes of bounded regions

Newman, James M.

doi:10.1090/S0002-9939-1972-0296480-8

Coercive inequalities for certain classes of bounded regions
HTML articles powered by AMS MathViewer

by James M. Newman PDF

Proc. Amer. Math. Soc. 32 (1972), 120-126 Request permission

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 ${R_2}$; 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 Hölder norm; here the results hold for complex-valued functions with no boundary conditions; the regions are bounded subdomains of ${R_n}$ having the cone property.

References

Shmuel Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. MR 0178246
Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, vol. 3, American Mathematical Society, Providence, R.I., 1979. With supplements by Lars Gȧrding and A. N. Milgram; With a preface by A. S. Householder; Reprint of the 1964 original. MR 598466
Djairo Guedes de Figueiredo, The coerciveness problem for forms over vector valued functions, Comm. Pure Appl. Math. 16 (1963), 63–94. MR 149082, DOI 10.1002/cpa.3160160109
Lars Gårding, Dirichlet’s problem for linear elliptic partial differential equations, Math. Scand. 1 (1953), 55–72. MR 64979, DOI 10.7146/math.scand.a-10364

Les méthodes directes en théorie des équations elliptiques

37

James M. Newman, Coercive inequalities for sectors in the plane, Comm. Pure Appl. Math. 22 (1969), 825–838. MR 268505, DOI 10.1002/cpa.3160220606
Martin Schechter, Coerciveness of linear partial differential operators for functions satisfying zero Dirichlet-type boundary data, Comm. Pure Appl. Math. 11 (1958), 153–174. MR 132911, DOI 10.1002/cpa.3160110202
K. T. Smith, Inequalities for formally positive integro-differential forms, Bull. Amer. Math. Soc. 67 (1961), 368–370. MR 142895, DOI 10.1090/S0002-9904-1961-10622-8