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Multipliers in weighted Sobolev spaces

Sbornik: Mathematics, 2005
Let \(X_1\) and \(X_2\) be a pair of Banach spaces of functions in \(\Omega\subset \mathbb R^n\). A function \(\gamma\) on \(\Omega\) such that \(\gamma X_1= \{ \gamma f\), \(f\in X_1\} \subset X_2\) is called a multiplier from \(X_1\) to \(X_2\). In the present paper, sufficient conditions on \(\gamma\) and weight functions ensuring that \(\gamma ...
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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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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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Embeddings of Sobolev Spaces with Weights of Power Type

Zeitschrift für Analysis und ihre Anwendungen, 1985
The paper deals with some properties of the weighted Sobolev spaces W_0^{k,p}, W_M^{k,p} and H^{k,p} , with weights which are powers of the distance from a part
Edmunds, David E., Kufner, Alois, Rákosník, Jiří   +2 more
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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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Optimal Control Problems in Sobolev Spaces with Weights

SIAM Journal on Control and Optimization, 1976
We consider an optimal control problem in certain Sobolev spaces with weights used systematically by F. Treves in [1], [2]. The notations and definitions are the same as in [2] and [3].
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Sobolev Spaces with Muckenhoupt Weights, Singularities and Inequalities

gmj, 2008
Abstract We use the recently introduced concept of growth envelopes to characterize weighted spaces of type , where 𝑤 belongs to some Muckenhoupt 𝐴𝑝 class, and discuss some applications.
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Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted p (·)-Laplacian

Complex Variables and Elliptic Equations, 2021
Cihan Ünal, Ismail Aydin
exaly  

WEIGHTED SOBOLEV SPACES

Bulletin of the London Mathematical Society, 1986
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