References
Dell, R.: Lower bounds for solutions to elliptic partial differential inequalities. Dissertation, University of California, Los Angeles, 1970.
Ladyzhenskaya, O. A., Ural'tseva, N.N.: Local estimates for gradients of solutions of nonuniformly elliptic and parabolic equations. Commun. Pure Appl. Math.22, 677–703 (1970).
Meyers, N., Serrin, J.: The exterior Dirichlet problem for second order elliptic differential equations. J. Math. Mech.9, 513–538 (1960).
Moser, J.: On Harnack's theorem for elliptic differential equations. Commun. Pure Appl. Math.14, 577–591 (1961).
Piepenbrink, J., Redheffer, R.: Nonlinear partial differential inequalities. Arch. Rat. Mech. Analysis36, 89–121 (1970).
Protter, M. H., Weinberger, H. F.: Maximum principles in differential equations. Englewood Cliffs, New Jersey: Prentice-Hall 1967.
Rademacher, H., Toeplitz, O.: The enjoyment of mathematics. Princeton, New Jersey: Princeton University Press 1957.
Serrin, J.: On the Harnack inequality for linear elliptic equations. J. Analyse Math.4, 292–308 (1956).
Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Roy. Soc. London264, 413–496 (1969).
Serrin, J.: A Harnack inequality for nonlinear equations. Bull. Amer. Math. Soc.69, 481–486 (1963).
Trudinger, N. S.: On Harnack type inequalities and their application to quasilinear elliptic equations. Commun. Pure Appl. Math.20, 721–747 (1967).
Author information
Authors and Affiliations
Additional information
Supported in part by NSF Grant GP-13377
Rights and permissions
About this article
Cite this article
Dell, R., Redheffer, R. Sharp lower bounds for solutions of nonlinear differential inequalities. Math Z 127, 199–216 (1972). https://doi.org/10.1007/BF01114924
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01114924