Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Some nonstandard problems for the Poisson equation


Authors: L. E. Payne and P. W. Schaefer
Journal: Quart. Appl. Math. 51 (1993), 81-90
MSC: Primary 35J05; Secondary 35A05
DOI: https://doi.org/10.1090/qam/1205938
MathSciNet review: MR1205938
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  • [1] G. E. Backus, Application of a non-linear boundary-value problem for Laplace's equation to gravity and geomagnetic intensity surveys, Quart. J. Mech. Appl. Math. XXI, 195-221 (1968) MR 0227444
  • [2] E. Hopf, Elementare Bemerkung über die Lösung partieller Differentialgleichung zweiter Ordnung von elliptischen Typus, Berlin Sber. Preuss. Akad. Wiss. 19, 147-152 (1927)
  • [3] -, A remark on elliptic differential equations of the second order, Proc. Amer. Math. Soc. 3, 791-793 (1952) MR 0050126
  • [4] B. Kawohl, Rearrangements and convexity of level sets in PDE, Lecture Notes in Math., vol. 1150, Springer-Verlag, Berlin and New York, 1985 MR 810619
  • [5] A. U. Kennington, Power concavity and boundary value problems, Indiana Univ. Math. J. 34, 687-704 (1985) MR 794582
  • [6] N. J. Korevaar, Convexity of level sets for solutions to elliptic ring problems, Comm. Partial Differential Equations 15, 541-556 (1990) MR 1046708
  • [7] R. Magnanini, A fully nonlinear boundary value problem for the Laplace equation, Lecture Notes Pure Appl. Math., vol. 109, Marcel Dekker, 1987, pp. 327-330 MR 912311
  • [8] -, A fully nonlinear boundary value problem for the Laplace equation in dimension two, Appl. Anal. 39, 185-192 (1990) MR 1095632
  • [9] L. G. Makar-Limanov, Solutions of Dirichlet's problem for the equation $ \Delta u = - 1$ on a convex region, Math. Notes 9, 52-53 (1971) MR 0279321
  • [10] L. E. Payne, Bounds for the maximum stress in the St. Venant torsion problem, Indian J. Mech. Math. (special issue) 51-59 (1968) MR 0351225
  • [11] L. E. Payne and G. A. Philippin, Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature, Nonlinear Anal. 3, 193-211 (1979) MR 525971
  • [12] -, Some applications of the maximum principle in the problem of torsional creep, SIAM J. Appl. Math. 33, 446-455 (1977) MR 0455738
  • [13] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43, 304-318 (1971) MR 0333220
  • [14] -, The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London 264, 413-496 (1969) MR 0282058
  • [15] -, Nonlinear elliptic equations of second order, Lectures in Sympos. Partial Differential Equations, Berkeley, 1971 (mimeographed notes)
  • [16] R. P. Sperb, Extension of two theorems of Payne to some nonlinear Dirichlet problems, J. Appl. Math. Phys. (ZAMP) 26, 721-726 (1975) MR 0393835
  • [17] -, Maximum principles and their applications, Math. in Science and Engineering, vol. 157, Academic Press, New York, 1981 MR 615561
  • [18] H. F. Weinberger, Remarks on the preceding paper of Serrin, Arch. Rational Mech. Anal. 43, 319-320 (1971) MR 0333221

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DOI: https://doi.org/10.1090/qam/1205938
Article copyright: © Copyright 1993 American Mathematical Society

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