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- In [[mathematics]], '''Sobolev spaces for planar domains''' are one of the principal techniques used in the theor ==Sobolev spaces with boundary conditions== ...58 KB (9,224 words) - 19:52, 14 November 2024
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- ...orman George Meyers]], states that [[smooth functions]] are dense in the [[Sobolev space]] <math>W^{k,p}(\Omega)</math> ...by Meyers and Serrin ended much confusion about the relationship of these spaces that existed in the literature before that time. It is surprising that this ...2 KB (298 words) - 12:19, 12 December 2024
- where {{math|{{!}}⋅{{!}}<sub>''r'',''p''</sub>}} denotes the [[Sobolev space|Sobolev]] semi-norm. ...uan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" ''Numerisch ...2 KB (329 words) - 17:22, 18 January 2023
- ...omials''' are [[orthogonal polynomials]] with respect to a [[Sobolev space|Sobolev]] [[inner product]], i.e. an inner product with [[derivative]]s. By having conditions on the derivatives, the Sobolev orthogonal polynomials in general no longer share some of the nice features ...3 KB (375 words) - 23:30, 20 March 2024
- {{Short description|Generalization of Sobolev spaces}} ...pace]]s, serve to generalize more elementary [[function space]]s such as [[Sobolev space]]s and are effective at measuring regularity properties of functions. ...3 KB (452 words) - 20:03, 25 January 2025
- In [[mathematics]], '''logarithmic Sobolev inequalities''' are a class of inequalities involving the norm of a functio ...thbb{R}^n. </math> Unlike classical [[Sobolev inequalities]], Gross's log-Sobolev inequality does not have any dimension-dependent constant, which makes it a ...3 KB (492 words) - 04:19, 24 January 2025
- ...ical analysis]], most spaces which arise in practice turn out to be Banach spaces as well. == Classical Banach spaces == ...2 KB (351 words) - 00:44, 27 July 2024
- In 2018, she was given a chair for function spaces at the [[University of Rostock]] before returning to her present position i ...007).{{r|esefs}} With Hans Triebel she also wrote ''Distributions, Sobolev Spaces, Elliptic Equations'' (EMS Textbooks in Mathematics, European Mathematical ...3 KB (372 words) - 06:26, 9 August 2024
- ...ound the norm of an element in one space with a combination norms in other spaces, such as [[Ladyzhenskaya's inequality]] and the [[Gagliardo–Nirenberg inter ...interpolation inequalities are the [[Hölder condition#Hölder spaces|Hölder spaces]]. ...7 KB (1,098 words) - 01:14, 27 January 2025
- ...ness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space. Ann. Inst. H. Poincaré Anal. Non Linéaire '''12''' (1995), 319–337.< ...g invariance in the problem, and is usually considered in the context of [[Sobolev space]]s. The term ''cocompact embedding'' is inspired by the notion of [[C ...5 KB (740 words) - 18:34, 2 June 2017
- In mathematics, a '''Sobolev mapping''' is a mapping between [[manifold]]s which has [[smoothness]] in s Sobolev mappings appear naturally in manifold-constrained problems in the [[calculu ...13 KB (1,861 words) - 11:28, 1 January 2025
- ...Lions–Magenes lemma''' (or '''theorem''') is the result in the theory of [[Sobolev space]]s of [[Banach space]]-valued functions, which provides a criterion f ...>\dot{u} \in L^{4/3}([0, T]; H^{-1})</math> (where <math>H^1</math> is a [[Sobolev space]], and <math>H^{-1}</math> is its [[dual space]], which is not enough ...3 KB (488 words) - 08:13, 10 May 2024
- *{{cite journal |author=Lozanov-Crvenković, Z |title= Kernel theorems for the spaces of tempered ultradistributions |journal= Integral Transforms and Special Fu ...order $$\Psi $$DOs: Composition with entire functions, new Shubin-Sobolev spaces, and index theorem |journal=Analysis and Mathematical Physics |year=2021 |v ...2 KB (274 words) - 02:35, 21 January 2023
- ...rly works developed the foundations of integration on infinite-dimensional spaces and analytic tools needed for quantum fields corresponding to classical fie ===Abstract Wiener spaces=== ...11 KB (1,482 words) - 04:07, 2 January 2025
- ...square root satisfies the following relation involving the [[Sobolev space|Sobolev ''H''<sup>1</sup>-norm]] and [[Lp space|''L''<sup>2</sup>-norm]] for suitab ...es. However, remember that the aim is to work in ''infinite''-dimensional spaces, and it is a fact that [[there is no infinite-dimensional Lebesgue measure] ...7 KB (1,099 words) - 11:53, 19 November 2024
- ...]. Like the ''L''<sup>''p''</sup> spaces, they are [[Banach space]]s. The spaces are named for [[Władysław Orlicz]], who was the first to define them in 193 ...ces, a variety of function spaces arising naturally in analysis are Orlicz spaces. One such space ''L'' log<sup>+</sup> ''L'', which arises in the ...12 KB (1,956 words) - 15:33, 25 February 2025
- {{About|the vector spaces of sequences and functions|the finite-dimensional vector space distance|Che ...the latter. As a Banach space they are the continuous dual of the Banach spaces <math>\ell_1</math> of absolutely summable sequences, and <math>L^1 = L^1(X ...5 KB (786 words) - 13:24, 25 June 2024
- ...e of [[trace operator|trace]] (that is, <math>u</math> is a limit in the [[Sobolev space]] <math>H^1(\Omega)</math> of a sequence of [[smooth function]]s that ...e = Generalised Gagliardo–Nirenberg inequalities using weak Lebesgue spaces and BMO ...5 KB (622 words) - 13:06, 23 October 2022
- ...een different methods of [[interpolation space|interpolation]] in [[Banach spaces]].<ref>{{cite journal |author=S. Kaijser |title=A New Proof of the Fundamen ...ref>{{cite journal |author=M. Cwikel and J. Peetre |title=Abstract K and J spaces |journal=J. Math. Pures Appl. |volume=60 |year=1981 |pages=1-50}}</ref> ...5 KB (767 words) - 16:13, 24 February 2025
- === Banach spaces === === Sobolev spaces === ...12 KB (2,056 words) - 09:03, 16 April 2024
- ...admit a notion of differential calculus. They are constructed as quotient spaces of {{math|[0, 1] × ''K''}} where ''K'' is a [[Cantor set]].<ref name="Laaks ...on any real number greater than 1. These examples are now known as Laakso spaces. ...5 KB (824 words) - 21:21, 8 January 2025