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Sharp lower bounds for solutions of nonlinear differential inequalities. (English) Zbl 0223.35041


MSC:

35J99 Elliptic equations and elliptic systems
35R45 Partial differential inequalities and systems of partial differential inequalities
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References:

[1] Dell, R.: Lower bounds for solutions to elliptic partial differential inequalities. Dissertation, University of California, Los Angeles, 1970.
[2] 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). · Zbl 0193.07202
[3] Meyers, N., Serrin, J.: The exterior Dirichlet problem for second order elliptic differential equations. J. Math. Mech.9, 513-538 (1960). · Zbl 0094.29701
[4] Moser, J.: On Harnack’s theorem for elliptic differential equations. Commun. Pure Appl. Math.14, 577-591 (1961). · Zbl 0111.09302
[5] Piepenbrink, J., Redheffer, R.: Nonlinear partial differential inequalities. Arch. Rat. Mech. Analysis36, 89-121 (1970). · Zbl 0201.13703
[6] Protter, M. H., Weinberger, H. F.: Maximum principles in differential equations. Englewood Cliffs, New Jersey: Prentice-Hall 1967. · Zbl 0153.13602
[7] Rademacher, H., Toeplitz, O.: The enjoyment of mathematics. Princeton, New Jersey: Princeton University Press 1957. · Zbl 0078.00114
[8] Serrin, J.: On the Harnack inequality for linear elliptic equations. J. Analyse Math.4, 292-308 (1956). · Zbl 0070.32302
[9] Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Roy. Soc. London264, 413-496 (1969). · Zbl 0181.38003
[10] Serrin, J.: A Harnack inequality for nonlinear equations. Bull. Amer. Math. Soc.69, 481-486 (1963). · Zbl 0137.06902
[11] Trudinger, N. S.: On Harnack type inequalities and their application to quasilinear elliptic equations. Commun. Pure Appl. Math.20, 721-747 (1967). · Zbl 0153.42703
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