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Quantitative propagation for solutions of elliptic equations – A. Logunov & E. Malinnikova – ICM2018

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    The equality sign in 3. For a general planar, open, convex set, in [ 31 ], in the Euclidean case, the author proves the following result:. Alter and V. Caselles, Uniqueness of the Cheeger set of a convex body, Nonlinear Anal.

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    Trombetti and P. Lions, Convex symmetrization and applications, Ann. Amar and G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients, Ann. Belloni, V. Ferone and B. Kawohl, Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators, Z. Busemann, The isoperimetric problem for Minkowski area, Amer. Buttazzo, S.

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    Guarino Lo Bianco and M. Marini, Sharp estimates for the anisotropic torsional rigidity and the principal frequency, J. Caselles, A. Chambolle, S. Moll and M.

    Cheeger, A lower bound for the smalles eigenvalue of the Laplacian, Problems in Analysis. Cozzi, A. Farina and E. Valdinoci, Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations, Comm. Crasta and A. Malusa, The distance function from the boundary in a Minkowski space, Trans. Cuesta and P. Della Pietra and N.

    Gavitone, Sharp bounds for the first eigenvalue and the torsional rigidity related to some anisotropic operators, Math. Gavitone, Symmetrization with respect to the anisotropic perimeter and applications, Math. Della Pietra, N. Gavitone and S. Guarino Lo Bianco, On functionals involving the torsional rigidity related to some classes of nonlinear operators, J. Differential Equations, in press.

    Gavitone and G. Piscitelli, On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators, Bull. Fonseca and S. Edinburgh Sect. A , no. Henrot, I. Lucardesi and G. Kajikiya, A priori estimate for the first eigenvalue of the p -Laplacian, Differential Integral Equations 28 , no. Kawohl and M. Convex Anal. Ladyzhenskaya and N.

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    Download Strict Convexity Of Level Sets Of Solutions Of Some Nonlinear Elliptic Equations

    Parini, An introduction to the Cheeger problem, Surv. Parini, Reverse Cheeger inequality for planar convex sets, J. Payne, Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function, Proc. A 88 , no. Payne and I. Stakgold, On the mean value of the fundamental mode in the fixed membrane problem, Appl.

    Protter, A lower bound for the fundamental frequency of a convex region, Proc. Notae 17 , 82— Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 , no. Ferone, C. Nitsch and C.