论文标题
改进的弗里德里奇不等式可用于下均匀嵌入
Improved Friedrichs inequality for a subhomogeneous embedding
论文作者
论文摘要
对于平滑有限的域$ω$和$ p \ geq q \ geq 2 $，我们建立了经典的弗里德里希人不等式的量化版本$ \ | \ | \ | \ | \ | _p^p^p -λ_1\ | U \ | U \ | U \ | U \ | _q^p \ | _q^p \ geq 0 $，$，$，$，$ u \ $ in $ in $ in $ in $ in $ in $，广义最小频率。我们应用了所获得的量化之一，以表明共振方程$-Δ_Pu =λ_1\ | | u \ | | _q^{p-q} | u | u |^{q-2} u + + f $与零dirichlet边界条件相关的较弱的解决方案具有$ f $ f $ pug $ orthogoNal of the $ f $ for $ f $ of the Minimizer of Minimizer of $λ__1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$λ_1$。
For a smooth bounded domain $Ω$ and $p \geq q \geq 2$, we establish quantified versions of the classical Friedrichs inequality $\|\nabla u\|_p^p - λ_1 \|u\|_q^p \geq 0$, $u \in W_0^{1,p}(Ω)$, where $λ_1$ is a generalized least frequency. We apply one of the obtained quantifications to show that the resonant equation $-Δ_p u = λ_1 \|u\|_q^{p-q} |u|^{q-2} u + f$ coupled with zero Dirichlet boundary conditions possesses a weak solution provided $f$ is orthogonal to the minimizer of $λ_1$.
