| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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.
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