Existence and regularity of functions which minimize certain energies in homotopy classes of mappings
Existence and regularity of functions which minimize certain energies in homotopy classes of mappings
复制标题
最小化映射同伦类中某些能量的函数的存在性和正则性
DOI：
10.3233/asy-1991-5203
复制
发表时间：
1991
期刊：
影响因子：
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通讯作者：
M. Fuchs
中科院分区：
文献类型：
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作者：
F. Duzaar;M. Fuchs
杜扎尔。F.和M.傅志华，同伦映射类中能量最小化函数的存在性与正则性，渐近分析5（1991）129-144。对于紧致流形上的连续映射P：M -> N，证明了当N的截面曲率为非正时，问题Ep（u），= fM I du I p dv -> Min在同伦类中存在可微解.这里p E [2，（0）]是一个任意的真实的数，因此我们得到了Eells和Sampson的一个著名定理的推广.我们的论点是基于一个渐近分析的退化问题（0分钟，在10 '1'1，我们建立的解决方案u的存在性，收敛到我们原来的变分问题的最小值。作为进一步的应用，本文包含各种估计的p-调和映射到负弯曲的目标流形。
Duzaar. F. and M. Fuchs, Existence and regularity of functions which minimize certain energies in homotopy classes of mappings, Asymptotic Analysis 5 (1991) 129-144. Given a continuous mapping 'P: M --> N of compact manifolds we prove that there exists a differentiable solution of the problem Ep(u) ,= fM I du I p dv -> Min in the homotopy class ['1'1 provided the sectional curvature of N is nonpositive. Here p E [2, (0) is an arbitrary real number, hence we obtain an extension of a well-known theorem of Eells and Sampson. Our arguments are based on an asymptotic analysis of the less degenerate problems (0 min in ['1'1 for which we establish the existence of solutions u, which converge to a minimizer of our original variational problem. As further applications the paper contains various estimates for p-harmonic maps into negatively curved target manifolds.