Sharp estimates for solutions to elliptic problems with mixed boundary conditions

Journal de Mathématiques Pures et Appliquées - Tập 152 - Trang 251-261 - 2020
A. Alvino1, F. Chiacchio1, C. Nitsch1, C. Trombetti1
1Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli, Italy

Tài liệu tham khảo

Alvino, 1997, Convex symmetrization and applications, Ann. Inst. Henri Poincaré, 14, 275, 10.1016/S0294-1449(97)80147-3 Alvino, 1990, Comparison results for elliptic and parabolic equations via Schwarz symmetrization, Ann. Inst. Henri Poincaré, 7, 37, 10.1016/S0294-1449(16)30303-1 Alvino Bennett, 1988, Interpolation of Operators, vol. 129 Bossel, 1988, Membranes élastiquement liées: inhomogènes ou sur une surface: une nouvelle extension du théorème isopérimétrique de Rayleigh-Faber-Krahn, Z. Angew. Math. Phys., 39, 733, 10.1007/BF00948733 Bucur, 2017, Symmetry breaking for a problem in optimal insulation, J. Math. Pures Appl., 107, 451, 10.1016/j.matpur.2016.07.006 Bucur, 2010, An alternative approach to the Faber-Krahn inequality for Robin problems, Calc. Var. Partial Differ. Equ., 37, 75, 10.1007/s00526-009-0252-3 Bucur, 2010, A variational approach to the isoperimetric inequality for the Robin eigenvalue problem, Arch. Ration. Mech. Anal., 198, 927, 10.1007/s00205-010-0298-6 Bucur, 2015, Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach, Arch. Ration. Mech. Anal., 218, 757, 10.1007/s00205-015-0872-z Daners, 2006, A Faber-Krahn inequality for Robin problems in any space dimension, Math. Ann., 333, 767, 10.1007/s00208-006-0753-8 Della Pietra, 2017, Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions, ESAIM Control Optim. Calc. Var., 23, 1381, 10.1051/cocv/2016058 Kawohl, 1985, Rearrangements and Convexity of Level Sets in PDE, vol. 1150 Kesavan, 1988, Some remarks on a result of Talenti, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4), 15, 453 Kesavan, 2006, Symmetrization & Applications, vol. 3 Talenti, 1976, Elliptic equations and rearrangements, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4), 3, 697