Skip to main content Accessibility help
×
Home

A priori bounds for a class of nonlinear elliptic equations and applications to physical problems

  • Catherine Bandle (a1)

Synopsis

Upper and lower bounds for the solutions of a nonlinear Dirichlet problem are given and isoperimetric inequalities for the maximal pressure of an ideal charged gas are constructed. The method used here is based on a geometrical result for two-dimensional abstract surfaces.

Copyright

References

Hide All
1Alexandrow, A. D.. Die innere Geometrie der konvexen Flächen (Berlin: Akademie Verlag, 1955).
2Bandle, C.. Existence theorems, qualitative results and a priori bounds for a class of nonlinear Dirichlet problems. Arch. Rational Mech. Anal. 58 (1975), 219238.
3Bandle, C.. Isoperimetric inequalities for a nonlinear eigenvalue problem. Proc. Amer. Math. Soc. 56 (1976), 243246.
4Bandle, C.. Estimates for the Green's functions of elliptic operators. SIAM J. Math. Anal. 9 (1978), 11261136.
5Bandle, C.. Isoperimetric inequalities and applications (Bath: Pitman, 1980).
6Gelfand, I. M.. Some problems in the theory of quasi-linear equations. Amer. Math. Soc. Transl. 29 (1963), 295381.
7Keller, J. B.. Electrohydrodynamics I. The equilibrium of a charged gas in a container. J. Rational Mech. Anal. 5 (1956) 715724.
8Payne, L. E.. Some isoperimetric inequalities in the torsion problem for multiply connected regions. In Studies in Mathematical Analysis and Related Topics, pp. 270280 (Stanford, Calif.: Stanford Univ. Press, 1962).
9Payne, L. E. and Stakgold, I.. Nonlinear problems in nuclear reactor analysis. Lecture Notes in Mathematics, 322 (Berlin: Springer, 1973).
10Pólya, G. and Szegö, G.. Isoperimetric inequalities in mathematical physics (Princeton, N.J.: Princeton Univ. Press, 1951).

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed