Rendiconti del Seminario Matematico della Università di Padova


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Volume 137, 2017, pp. 155–184
DOI: 10.4171/RSMUP/137-8

A construction of a uniform continuous minimizing movement associated with a singular functional

Yoshihiko Yamaura[1]

(1) Department of Mathematics, Nihon University, 3-25-40, Sakurajosui, Setagaya-ku, 156-8550, Tokyo, Japan

A minimizing movement is constructed associated with a singular functional introduced by Alt and Caffarelli in order to study a free boundary problem. The main purpose of the present research is to construct a minimizing movement, which is uniformly continuous with respect to both time and space variables. The strategy is to regularize the singular term of time discretized functionals, and then to pass to the limit in the regularization parameter in the sense of €$\Gamma$-convergence keeping the time discretization parameter fixed.

Keywords: Minimizing movement, free boundary problem, €$\Gamma$-convergence

Yamaura Yoshihiko: A construction of a uniform continuous minimizing movement associated with a singular functional. Rend. Sem. Mat. Univ. Padova 137 (2017), 155-184. doi: 10.4171/RSMUP/137-8