ON SOME EXTENSIONS OF RELLICH'S INEQUALITY
Main Article Content
In this note we derive some new inequalities which in the special cases yields an extension of Rellich's inequality recently given by Bennett.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
R. A. Adams, "Sobolev spaces", Academic Press, New York, 1975.
W. Allegretto, "Nonoscillation theory of elliptic equations of order 2n", Pacific J. Math. 64, 1-16, 1976.
D. M. Bennett, "An extension of Rellich's inequality", Proc. Amer. Math. Soc. 106, 987-993, 1989.
D. C. Benson, "Inequalities involving integrals of functions and their derivatives", J. Math. Anal. Appl. 17, 292-308, 1967.
F. Bernis, "Compactness of the support for some nonlinear elliptic problems of arbitrary order in dimension N", Comm. Partial Di.ff. Eqs. 9, 271-312, 1984.
J. A. Dubinskii, "Some integral inequalities and the solvability of degenerate quasilinear elliptic systems of differential equations", Math. Si. 64, 458-480, 1964.
B. G. Pachpatte, "On Sobolev type integral inequalities", Proc. Royal. Soc. Edinburgh 103A, 1-14, 1986.
B. G. Pachpalte, "A note on Dubinskii type inequality", Libertas Mathematica 9, 49-57, 1989.
F. Rellich, "Perturbation theory of eigenvalue problems", Gordon and Breach, New York, 1969.
U. W. Schmincke, "Essential self-adjointness of a Schrodinger operator with strongly singular potential", Math. Z. 124, 47-50, 1972.