Nonlinear diffusion equations and curvature conditions in metric measure spaces / Luigi Ambrosio, Andrea Mondino, Giuseppe Savaré.

Format:

Book

Author/Creator:

Ambrosio, Luigi, author.

Mondino, Andrea, 1984- author.

Savaré, Giuseppe, author.

Series:

Memoirs of the American Mathematical Society ; no. 1270.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1270

Language:

English

Subjects (All):

Differential calculus.

Physical Description:

v, 121 pages : illustrations ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, [2019]

Summary:

Aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, our new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, our new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD*(K,N) condition of Bacher-Sturm.

Notes:

"November 2019; Volume 262; number 1270 (seventh of 7 numbers)."

Includes bibliographical references (pages 119-121).

ISBN:

9781470439132

1470439131

OCLC:

1121159623