Skip to main content
Article thumbnail
Location of Repository

Characterization of subdifferentials of a singular convex functional in Sobolev spaces of order minus one

By Yohei Kashima

Abstract

Subdifferentials of a singular convex functional representing the surface free energy of a crystal under the roughening temperature are characterized. The energy functional is defined on Sobolev spaces of order -1, so the subdifferential mathematically formulates the energy's gradient which formally involves 4th order spacial derivatives of the surface's height. The subdifferentials are analyzed in the negative Sobolev spaces of arbitrary spacial dimension on which both a periodic boundary condition and a Dirichlet boundary condition are separately imposed. Based on the characterization theorem of subdifferentials, the smallest element contained in the subdifferential of the energy for a spherically symmetric surface is calculated under the Dirichlet boundary condition.Comment: 26 page

Topics: Mathematics - Analysis of PDEs, 47J30 (Primary) 35G20, 35R70 (Secondary)
Year: 2011
OAI identifier: oai:arXiv.org:1104.3649
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1104.3649 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.