Breaking of symmetry in poisson equation

References

• Alvino , A. , Lions , P. L. and Trombetti , G. 1990 . Comparison results for elliptic and parabolic equations via symmetrization . Ann. Inst. Henri Poincaré Analyse non linére , 7 ( 2 )
   Google Scholar
• Bandle , C. 1976 . On symmetrization in parabolic problems . J. Analyse Math. , 30 ( 2 )
   Google Scholar
• Cianchi , A. 1992 . Maximizing the L∞ norm of the gradient of solutions to Poisson equations . The JOurnal of Geometric Analysis , 2 ( 6 )
   Google Scholar
• Cianchi , A. 1985 . “ Applications of geometric rearrangements to certain nonlinear elliptic equations with free boundary, Nonlinear Differential Equations ” . In Res. Notes in Math. , Vol. 132 , Boston, MA-London : Pitman . Granada 1984
   Google Scholar
• Kawohl , B. 1985 . “ Rearrangements and convexity of level sets in PDE ” . In Lecture Notes in Math. , Vol. 1150 , Berlin : Springer–Verlag .
   Google Scholar
• Mossino , J. 1984 . Inégalité isopérimetriques et applications en physique , Paris : Herman .
   Google Scholar
• Müller , C. 1966 . “ Spherical Harmonics ” . In Lecture Notes in Math. , Vol. 17 , Berlin : Springer–Verlag .
   Google Scholar
• Talenti , G. 1976 . Elliptic equations and rearrangements . Ann. Sc. Norm. Sup. Pisa , 3 ( 4 )
   Google Scholar
• Zeidler , E. 1985 . Nonlinear Functional Analysis and its Applications III , Berlin : Springer–Verlag .
   Google Scholar