Global Morrey regularity results for asymptotically convex variational problems
Global Morrey regularity results for asymptotically convex variational problems
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渐近凸变分问题的全局 Morrey 正则结果
DOI：
10.1515/forum.2008.043
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Verde
中科院分区：
文献类型：
--
作者：
M. Foss;A. P. di Napoli;A. Verde
摘要 我们证明了 Ω ⊂ ℝ n 域边界的一些全局连续性和 Morrey 正则性结果，适用于 形式的泛函的几乎最小化。主要假设是 g 是渐近凸的，并且它关于其第三个参数具有超线性多项式增长。被积函数仅需要相对于其第三个参数是局部有界的。相对于其他参数的一些不连续行为也是允许的。我们还将我们的结果应用于一类带有障碍的变分问题。
Abstract We prove some global, up to the boundary of a domain Ω ⊂ ℝ n , continuity and Morrey regularity results for almost minimizers of functionals of the form . The main assumptions are that g is asymptotically convex and that it has superlinear polynomial growth with respect its third argument. The integrand is only required to be locally bounded with respect to its third argument. Some discontinuous behavior with respect to its other arguments is also allowed. We also provide an application of our results to a class of variational problems with obstacles.