Some Estimates for the Symmetrized First Eigenfunction of the Laplacian

Potential Analysis

Volumn 9, Issue 2, 1998, Pages 143-173

  Bhattacharya, T ^a   Weitsman, A ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Eigenfunctions; Eigenvectors; Partial differential equations; Symmetrization

Indexed keywords

EID: 0032357354     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1017997125764     Document Type: Article

References (10)

1. Bandle, C.: Isoperimetric Inequalities and Applications, Pitman Monographs and Studies in Math., 7, Boston, 1980.
2. Chavel, I.: Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984.
3. Chiti, G.: 'A reverse Hölder inequality for the eigenfunctions of linear second order elliptic operators', J. Appl. Math. and Phys. (ZAMP) 33 (1982), 143-148.
4. Chiti, G.: 'An isoperimetric inequality for the eigenfunctions of linear second order elliptic operators', Boll. Un. Mat. Ital. (6) 1-A (1982), 145-151.
5. Federer, H.: Geometric Measure Theory, Springer-Verlag, Berlin, 1969.
6. Kawohl, B.: Rearrangements and Convexity of Level Sets in PDE, Lect. Notes in Math. 1150, Springer-Verlag, Berlin, 1985.
7. Pólya, G. and Szegö, G.: Isoperimetric inequalities in Mathematical Physics, Ann. of Math. Studies 27, Princeton Univ. Press, Princeton, 1951.
8. Talenti, G.: 'Elliptic equations and rearrangements', Ann. Scuola. Norm Supp. Pisa (4) 3 (1976), 697-718.
9. Talenti, G.: 'Nonlinear Elliptic Equations, Rearrangements of Functions and Orlicz Spaces', Ann. Mat. Pura. Appl. 120 (1979), 159-184.
10. Watson, G. N.: A Treatise on the Theory of Bessel Functions. 2nd ed. Cambridge Univ. Press, Cambridge, 1944.