Maximum Principles and the Symmetry of Solutions for Parabolic Fractional p(x,·)-Equations in Exterior Domains
Анотація
У цій роботі ми спочатку встановлюємо деякі принципи максимуму, зокрема простий принцип максимуму, принцип максимуму для параболічних дробових $p(x,\cdot)$-лапласіанів та принцип максимуму для антисиметричних функцій. Далі ми розглядаємо лему Гопфа для параболічних дробових $p(x,\cdot)$-лапласіанів, яка є узагальненням результатів із праці Ванга-Ченя [Commun. Pure Appl. Anal. 21 (2022) 3055--3069]. Наприкінці, застосовуючи принцип максимуму для антисиметричних функцій та метод рухомих площин, ми отримуємо симетрію та монотонність розв'язків нелінійних параболічних дробових $p(x,\cdot)$-рівнянь у зовнішніх областях кулі. З сподіванням надати нові перспективи та інструменти для подальших досліджень.
Mathematical Subject Classification 2020: 35R11, 35K55, 35B50
Ключові слова:
параболічні дробові $p(x,\cdot)$-лапласіани, зовнішні області, принцип максимуму для антисиметричних функці, лема Гопфа, симетрія та монотонністьПосилання
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