Geodesic
Isoperimetric Inequalities for the Principal Eigenvalue of a Membrane and the Energy of Problems with Robin Boundary Conditions
Journal of convex analysis, Tome 22 (2015) no. 3, pp. 627-64
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An inequality for the reverse Bossel-Daners inequality is derived by means of the harmonic transplantation. The first and second shape derivatives are computed for the ball. The same method is then applied to elliptic boundary value problems with inhomogeneous Neumann conditions. The first variation is computed and an isoperimetric inequality is derived for the minimal energy.
Classification : 49K20, 49R05, 15A42, 35J20, 35N25
Mots-clés : Rayleigh-Faber Krahn inequality, Robin boundary conditions, domain variation, harmonic transplantation 
@article{JCA_2015_22_3_JCA_2015_22_3_a1,
     author = {C. Bandle and A. Wagner},
     title = {Isoperimetric {Inequalities} for the {Principal} {Eigenvalue} of a {Membrane} and the {Energy} of {Problems} with {Robin} {Boundary} {Conditions}},
     journal = {Journal of convex analysis},
     pages = {627--64},
     year = {2015},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a1/}
}
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C. Bandle; A. Wagner. Isoperimetric Inequalities for the Principal Eigenvalue of a Membrane and the Energy of Problems with Robin Boundary Conditions. Journal of convex analysis, Tome 22 (2015) no. 3, pp. 627-64. http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a1/