Regularity for the evolutionary p-Laplace operator and global existence of the p-harmonic map flows

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540215
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kumamoto University
• Principal Investigator: MISAWA MASASHI 熊本大学, 自然科学研究科, 教授 (40242672)
• Co-Investigator(Renkei-kenkyūsha): YAMAURA Yoshihiko 日本大学, 文理学部, 教授 (90255597)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 偏微分方程式 / 退化特異放物型作用素 / 正則性特異性 / 調和写像 / 調和写像熱流 / p調和写像 / p調和写像熱流

Outline of Final Research Achievements

We have been studied the regularity problem for p-harmonic map heat flows. The p-harmonic maps are critical points for p-energy for maps beteween two smooth compact Riemannian manifolds and so, the solution of the Euler Lagrange equation of p-energy, which is 2nd ordered degenerate and singular elliptic partial differential equations of so-called p-Laplcian type. In this research project we will study the existence and regularity of solutions of the p-harmonic map equations. In particular, we study the evolution equation, called the p-harmonic map heat flow. Our main result is to show the regularity of small solutions of the p-harmonic map heat flows. Under this main result, we also to show the regularity and existence of a global small solution of the m-harmonc map type heat flows with space dimension m. The asymptotic behavior to the stationary solution is also shown.

Free Research Field

偏微分方程式