Existence Results for Some Anisotropic Elliptic Problems Having Variable Exponent and L1-data
DOI:
https://doi.org/10.15407/mag19.04.696Ключові слова:
анізотропний, змінний показник, простір Соболєва, нелінійна еліптична проблема, метод штрафних функцій, ентропійні розв'язкиАнотація
У роботі ми вивчаємо існування ентропійних розв'язків для сильно нелінійного анізотропного еліптичного рівняння
$$
Au+ H(x,u,\nabla u) = f\qquad \mbox{in}\quad \Omega,
$$
де $f$ належить $L^{1}(\Omega)$, $A$ є оператором Лере-Ліонса, і $H$ є нелінійним членом нижчого порядку зростання відносно $|\nabla u|$ (тобто таким, що $|H(x,s,\xi)|\leq c(x) + b(|s|)\sum_{i=1}^{N}|\xi_{i}|^{p_{i}(x)}),$ але без припущення, що $H(x,s,\xi)s\geq0$. Наведено конкретний приклад, що ілюструє результат існування розв'язків.
Mathematical Subject Classification 2020: 35J60, 46E35, 35D35
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