Bounded Solutions to Strongly Nonlinear Elliptic Problems without Sign Restrictions in Weighted Sobolev Spaces
Анотація
У цій роботі ми досліджуємо існування та $L^\infty$-регулярність розв'язків для загального класу сильно нелінійних еліптичних задач, пов'язаних із диференціальним включенням
\begin{equation*}
\gamma(u) + A(u) + \Phi(x,u,\nabla u) \ni f,
\end{equation*}
де $A$ є оператором Лере-Ліонса з $W^{1,p}_0(\Omega,\omega)$ у його спряжений простір $W^{-1,p'}(\Omega,\omega^*)$, $\gamma$ є максимальним монотонним відображенням з $0 \in \gamma(0)$, $\Phi$ є нелінійним членом, що задовольняє лише умову росту без жодних обмежень на знак щодо $s$, а права частина $f$, як передбачається, належить до $L^\infty(\Omega)$.
Mathematical Subject Classification 2020: 35J66, 35A15, 35D30
Ключові слова:
задачі про включення, $L^{\infty}$-оцінка, $p$-зростання, слабкий розв'язок, вагові простори СоболєваПосилання
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