共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the Γ-convergence of the following functional (p > 2)
$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2,$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2, 相似文献
2.
Andreas Fleige 《Integral Equations and Operator Theory》1999,33(1):20-33
By Kato's First and Second Representation Theorem a closed densely defined semibounded hermitian sesquilinear form [·,·] in a Hilbert spaceH can be represented by a selfadjoint operatorT inH and if, in particular, the formt[·,·] is nonnegative thenD(t)=D(T
1/2
). In the present note this result is generalized to non-semibounded forms by means of Krein space methods. An application to the form
where the functionp changes its sign leads to an expansion theorem for the Sturm-Liouville problem –(pu)=u,u(a)=u(b)=0 with respect to the weighted Sobolev norm
. 相似文献
3.
Mónica Clapp Andrzej Szulkin 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):229-248
We consider the magnetic nonlinear Schrödinger equations $\begin{array}{ll}{\left(-i\nabla + sA\right)^{2} u + u \, = \, |u|^{p-2}\, u, \quad p \in (2, 6),} \\ \quad \quad {\left(-i\nabla + sA\right) ^{2}u \, = \, |u|^{4}\, u,}\end{array}$ in ${\Omega=\mathcal{O}\times \mathbb{R}}
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