多相椭圆问题弱解的全局正则性

doi:10.6040/j.issn.1671-9352.0.2024.376

摘要/Abstract

摘要： 研究与多相泛函相对应的非一致椭圆方程弱解的全局正则性。利用Young不等式、Hölder不等式、Sobolev-Poincaré不等式、Gehring引理等,提高了可积指数,获得了该方程弱解的全局正则性。

Abstract: Global regularity of weak solutions to the nonlinear elliptic equations corresponding to multi-phase functionals is considered. By using the Young inequality, the Hölder inequality, the Sobolev-Poincaré inequality and the Gehring lemma, the integrable exponent is improved. The global regularity of the weak solution of the equation is obtained.

Key words: regularity, elliptic problem, weak solution, multi-phase

中图分类号:

O175

马梦璐,要佳慧,佟玉霞. 多相椭圆问题弱解的全局正则性[J]. 《山东大学学报(理学版)》, 2026, 61(7): 123-133.

MA Menglu, YAO Jiahui, TONG Yuxia. Global regularity of weak solutions to multi-phase elliptic problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(7): 123-133.

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