Natural boundary value problems for weighted form laplacians

Wojciech Kozłowski; Antoni Pierzchalski

Displaying similar documents to “Natural boundary value problems for weighted form laplacians”

The Properties of the Weighted Space $H_{2, α}^{k} (Ω)$ and Weighted Set $W_{2, α}^{k} (Ω, δ)$

V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)

Communications in Mathematics

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We study the properties of the weighted space $H_{2, α}^{k} (Ω)$ and weighted set $W_{2, α}^{k} (Ω, δ)$ for boundary value problem with singularity.

The representation of multi-hypergraphs by set intersections

Stanisław Bylka, Jan Komar (2007)

Discussiones Mathematicae Graph Theory

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This paper deals with weighted set systems (V,,q), where V is a set of indices, $\subset 2^{V}$ and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family $R = {(R_{v})}_{v \in V}$ of subsets of a set S such that $| ⋂_{v \in E} R_{v} | = q (E)$ for each E ∈ . A necessary condition...

Solutions to the equation div u = f in weighted Sobolev spaces

Katrin Schumacher (2008)

Banach Center Publications

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We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with $\int_{Ω} f = 0$ is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces $W_{w}^{k, q} (Ω)$ , where the weight function w is in the class of Muckenhoupt weights $A_{q}$ .

Note on duality of weighted multi-parameter Triebel-Lizorkin spaces

Wei Ding, Jiao Chen, Yaoming Niu (2019)

Czechoslovak Mathematical Journal

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We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces ${\dot{F}}_{p}^{α, q} (ω; ℝ^{n_{1}} \times ℝ^{n_{2}})$ . This space has been introduced and the result ${({\dot{F}}_{p}^{α, q} (ω; ℝ^{n_{1}} \times ℝ^{n_{2}}))}^{*} = {CMO}_{p}^{- α, q^{'}} (ω; ℝ^{n_{1}} \times ℝ^{n_{2}})$ for $0 < p \leq 1$ has been proved in Ding, Zhu (2017). In this paper, for $1 < p < \infty$ , $0 < q < \infty$ we establish its dual space ${\dot{H}}_{p}^{α, q} (ω; ℝ^{n_{1}} \times ℝ^{n_{2}})$ .

Boundary blow-up solutions for a cooperative system involving the p-Laplacian

Li Chen, Yujuan Chen, Dang Luo (2013)

Annales Polonici Mathematici

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We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_{p} u = g (u - α v), Δ_{p} v = f (v - β u)$ in a smooth bounded domain of $ℝ^{N}$ , where $Δ_{p}$ is the p-Laplacian operator defined by $Δ_{p} u = {d i v (| \nabla u |}^{p - 2} \nabla u)$ with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.

Essential norms of weighted composition operators between Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞

R. Demazeux (2011)

Studia Mathematica

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We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.

Existence of solutions to the (rot,div)-system in $L_{p}$ -weighted spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, ${v \cdot n ̅ |}_{S} = 0$ , S = ∂Ω in weighted $L_{p}$ -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.

Characterizations of $H_{x} 1$ -sufficiency of jets

Le Tien Tam (1986)

Annales Polonici Mathematici

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Existence and regularity of solutions of some elliptic system in domains with edges

Wojciech M. Zajączkowski

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CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in $D_{ϑ}$ ...............................................346. Existence of solutions of (3.14) in $H_{μ}^{k} (D_{ϑ})$ ............417. Green function................................................................528....

Weighted Frobenius-Perron operators and their spectra

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2017)

Mathematica Bohemica

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First, some classic properties of a weighted Frobenius-Perron operator $𝒫_{ϕ}^{u}$ on $L^{1} (Σ)$ as a predual of weighted Koopman operator $W = u U_{ϕ}$ on $L^{\infty} (Σ)$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of $𝒫_{ϕ}^{u}$ under certain conditions.

Continuous pluriharmonic boundary values

Per Åhag, Rafał Czyż (2007)

Annales Polonici Mathematici

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Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.

Weighted $H^{p}$ spaces

José García-Cuerva

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CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted $H^{p}$ spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................

Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl (2014)

Studia Mathematica

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We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space $^{(ω)}$ and the Roumieu space $^{ω}$ as intersection and union of spaces $^{(M)}$ and $^{M}$ for associated weight sequences, respectively.

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona

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We consider functionals of a potential energy $ℙ_{ψ} (u)$ corresponding to $𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚$ . We are dealing with $𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒$ with $𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠$ . Various types of the subsoil of the plate are described by various types of the $𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒$ nonlinear term $ψ (u)$ . The aim of the paper is to find a suitable computational algorithm.

Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

Dorothee D. Haroske (2011)

Banach Center Publications

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We study continuity envelopes of function spaces $B_{p, q}^{s} (ℝ ⁿ, w)$ and $F_{p, q}^{s} (ℝ ⁿ, w)$ where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.

The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces

Suying Liu, Minghua Yang (2018)

Czechoslovak Mathematical Journal

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Let $L$ be a non-negative self-adjoint operator acting on $L^{2} (ℝ^{n})$ satisfying a pointwise Gaussian estimate for its heat kernel. Let $w$ be an $A_{r}$ weight on $ℝ^{n} \times ℝ^{n}$ , $1 < r < \infty$ . In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H_{L, w}^{p} (ℝ^{n} \times ℝ^{n})$ , $0 < p \leq 1$ associated to $L$ . Based on the atomic decomposition, we show the dual relationship between $H_{L, w}^{1} (ℝ^{n} \times ℝ^{n})$ and ${BMO}_{L, w} (ℝ^{n} \times ℝ^{n})$ .