This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a consequence, we can for instance obtain parabolic power concavity of solutions to a general class of parabolic equations. Our results are applicable to the Pucci operator, the normalized q-Laplacians with 1
Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations / Ishige K.; Liu Q.; Salani P.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 141:(2020), pp. 342-370. [10.1016/j.matpur.2019.12.010]
Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations
Ishige K.;Liu Q.
;Salani P.
2020
Abstract
This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a consequence, we can for instance obtain parabolic power concavity of solutions to a general class of parabolic equations. Our results are applicable to the Pucci operator, the normalized q-Laplacians with 1
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