Results 161 to 170 of about 27,468 (197)

Nonlinear Elliptic Equations on Weighted Sobolev Space

Mathematical Notes, 2023
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Kumari, Rupali, Kar, Rasmita
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On Weighted Sobolev Spaces

Canadian Journal of Mathematics, 1996
AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are
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Weighted Sobolev spaces

Sbornik: Mathematics, 1998
Summary: The case when smooth functions are not dense in a weighted Sobolev space \(W\) is considered. New examples of the inequality \(H\neq W\) (where \(H\) is the closure of the space of smooth functions) are presented. We pose the problem of `viscosity' or `attainable' spaces \(V\) (that is, spaces that are in a certain sense limits of weighted ...
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Null-Sets Criteria for Weighted Sobolev Spaces

Journal of Mathematical Sciences, 2003
The authors give functional, capacity and metric characterizations of null sets on weighted Sobolev spaces \(L^1_{p,w}(G)\), with \(G\) an open subset of the \(n\)-dimensional Euclidean space. The weights are the usual Muckenhoupt \(A_p\) weights, and the norm on \(L^1_{p,w}(G)\) is given by \[ \int_G | \nabla u| ^p w \, dx.
Demshin, I. N., Dymchenko, Yu. V., Shlyk, V. A.   +2 more
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Imbedding Theorems for Weighted Orlicz-Sobolev Spaces

Journal of the London Mathematical Society, 1992
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Krbec, Miroslav, Opic, Bohumír, Pick, Luboš   +2 more
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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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Bases in Sobolev weight spaces

Mathematical Notes, 2000
The author constructs smooth spline bases for weighted Sobolev spaces on the square extending earlier work by Ciesielski and other mathematicians.
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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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Poincaré inequalities in weighted Sobolev spaces

Applied Mathematics and Mechanics, 2006
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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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