caa a22 4500 605515875 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0880-z doi (NATIONALLICENCE)springer-10.1007/s00205-015-0880-z Nonlocal Curvature Flows [Elektronische Daten] [Antonin Chambolle, Massimiliano Morini, Marcello Ponsiglione] This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible generalized curvature. Within this class, we implement a minimizing movements scheme and we prove that it approximates the viscosity solution of the corresponding level set PDE. We also describe several examples and applications. Besides recovering and presenting in a unified way existence, uniqueness, and approximation results for several geometric motions already studied and scattered in the literature, the theory developed in this paper also allows us to establish new results. Springer-Verlag Berlin Heidelberg, 2015 Chambolle Antonin CMAP, Ecole Polytechnique, CNRS, Palaiseau, France aut Morini Massimiliano Dip. di Matematica, Univ. Parma, Parma, Italy aut Ponsiglione Marcello Dip. di Matematica, Univ. Roma-I "La Sapienza”, Rome, Italy aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1263-1329 0003-9527 218:3<1263 2015 218 205 https://doi.org/10.1007/s00205-015-0880-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0880-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chambolle Antonin CMAP, Ecole Polytechnique, CNRS, Palaiseau, France aut NATIONALLICENCE 700 1- Morini Massimiliano Dip. di Matematica, Univ. Parma, Parma, Italy aut NATIONALLICENCE 700 1- Ponsiglione Marcello Dip. di Matematica, Univ. Roma-I "La Sapienza”, Rome, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1263-1329 0003-9527 218:3<1263 2015 218 205