Results 171 to 180 of about 27,220 (202)

Bifurcation in weighted Sobolev spaces

Nonlinearity, 2008
When P(x, ?) is a second order linear elliptic differential operator on many bifurcation problems P(x, ?)u ? ?u + f(x, u) = 0 cannot be formulated as a functional equation from to irrespective of p [1, ?], either because the Nemystskii operator f (u) := f(x, u) does not map W2,p to Lp due to the growth of f as |x| ? ? or because, while well defined,
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Poincaré inequalities in weighted Sobolev spaces

Applied Mathematics and Mechanics, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Wanyi, Sun, Jiong, Zheng, Zhiming
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INVERSE POWER METHOD AND WEIGHTED SOBOLEV SPACES

Acta Mathematica Scientia, 1992
The author studies the semilinear elliptic equation \(\Delta u+a(x)u=\lambda Q(x)f(u)\) in \(\mathbb{R}^ n\), where \(a(x)\), \(Q(x)\) are nonnegative continuous functions satisfying \(\lim_{| x|\to\infty}a(x)=a_ 0>0\), \(\lim_{| x|\to\infty}Q(x)=\overline Q>0\).
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Approximation in Weighted Sobolev Spaces

2011
For p≥1 we define L m,p (ℝ n ) as the set of distributions u on ℝ n such that $$\|u\|_{m, p}=\Biggl(\, \sum^m_{k=1} \int\bigl|\nabla_k u(x)\bigr |^p\, \mathrm{d}x\Biggr)^{1/p}
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Compact traces in weighted Sobolev spaces

Analysis, 1998
Summary: We study trace operators \(W^{1,p}(\Omega; v_0,v_1)\to L^q(\partial\Omega; w)\) in weighted Sobolev spaces for sufficiently regular unbounded domains \(\Omega\subset \mathbb{R}^N\) with noncompact boundary. We show that under certain conditions on the weight functions \(v_0\), \(v_1\), \(w\), this operator is compact.
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Interpolation of weighted Sobolev spaces

2000
Let \(\Omega\) be a domain of the space \(\mathbb R^n\), let \(\omega(x)\) and \(\{\omega_\alpha(x)\}\) be positive continuous functions on \(\Omega\), and let \(H^m_{p\psi}(\Omega)\) and \(L_{p,\omega}(\Omega)\) be weighted spaces with the respective norms \[ \begin{gathered} \|u\|_{H^m_{p,\psi}(\Omega)}= \left(\sum_{|\alpha|\leq m}\omega_\alpha(x)|D^\
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Elliptic Operators in Weighted Sobolev Spaces

2000
In this chapter, we prove some estimates for solutions of elliptic problems in weighted Sobolev spaces. The aim here is not to provide a thorough description of the theory of elliptic operators in weighted Sobolev spaces but rather to provide simple proofs of some results that are needed in subsequent chapters.
Frank Pacard, Tristan Rivière
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Spaces of weighted symbols and weighted sobolev spaces on manifolds

1987
This paper gives an approach to pseudodifferential operators on noncompact manifolds using a suitable class of weighted symbols and Sobolev spaces introduced by H.O. Cordes on ℙ. Here, these spaces are shown to be invariant under certain changes of coordinates. It is therefore possible to transfer them to manifolds with a compatible structure.
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WEIGHTED SOBOLEV SPACES

Bulletin of the London Mathematical Society, 1986
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Weighted Sobolev spaces and capacity

1994
The author considers the connection between a capacity and the pointwise definition in Sobolev spaces involving \(A_ p\)-class weights. He shows that Sobolev functions possess Lebesgue points quasi everywhere with respect to an appropriate capacity.
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