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Shaposhnikova, Tatyana
Alternative names
Publications (10 of 34) Show all publications
Shaposhnikova, T. (2012). Inequality for entire functions involving their maximum modulus and maximum term. Rendiconti Lincei - Matematica e Applicazioni, 23(3), 259-265
Open this publication in new window or tab >>Inequality for entire functions involving their maximum modulus and maximum term
2012 (English)In: Rendiconti Lincei - Matematica e Applicazioni, ISSN 1120-6330, E-ISSN 1720-0768, Vol. 23, no 3, p. 259-265Article in journal (Refereed) Published
Abstract [en]

An estimate of the Wiman-Valiron type for a maximum modulus on a polydisk of an entire function of several complex variables is obtained. The estimate contains a weight function involved also in the calculation of the radius of the admissible ball.

Place, publisher, year, edition, pages
European Mathematical Society, 2012
Keywords
Entire function, several complex variables, maximal modulus and maximum term
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-84366 (URN)10.4171/RLM/627 (DOI)000308218000002 ()
Available from: 2012-10-05 Created: 2012-10-05 Last updated: 2017-12-07
Mazya, V. & Shaposhnikova, T. (2011). Brezis-Gallouet-Wainger type inequality for irregular domains. Complex Variables and Elliptic Equations, 56(10), 991-1002
Open this publication in new window or tab >>Brezis-Gallouet-Wainger type inequality for irregular domains
2011 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 56, no 10, p. 991-1002Article in journal (Refereed) Published
Abstract [en]

A Brezis–Gallouet–Wainger logarithmic interpolation-embedding inequality is proved for various classes of irregular domains, in particular, for power cusps and λ-John domains.

Place, publisher, year, edition, pages
Taylor & Francis, 2011
Keywords
logarithmic interpolation inequalities, Sobolev embeddings, capacities
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-72153 (URN)10.1080/17476933.2010.538843 (DOI)000299695000010 ()
Available from: 2011-11-18 Created: 2011-11-18 Last updated: 2017-12-08Bibliographically approved
Mazya, V. & Shaposhnikova, T. (2011). Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains. Bulletin of Mathematical Sciences, 1(1), 33-77
Open this publication in new window or tab >>Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains
2011 (English)In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615, Vol. 1, no 1, p. 33-77Article in journal (Refereed) Published
Abstract [en]

This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains. Asymptotic properties of solutions at a point of a Lipschitz boundary are also discussed.

Keywords
Higher order elliptic equations – Higher order elliptic systems – Besov spaces – BMO – VMO – Lipschitz graph domains – Green’s function – Asymptotic behaviour of solutions
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-72623 (URN)10.1007/s13373-011-0003-6 (DOI)
Available from: 2011-12-01 Created: 2011-12-01 Last updated: 2017-12-08Bibliographically approved
Maz´ya, V., Mitrea, M. & Shaposhnikova, T. (2010). The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients. Journal d’Analyse Mathématique, 110(1), 167-239
Open this publication in new window or tab >>The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients
2010 (English)In: Journal d’Analyse Mathématique, ISSN 0021-7670, Vol. 110, no 1, p. 167-239Article in journal (Refereed) Published
Abstract [en]

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

Place, publisher, year, edition, pages
Springer, 2010
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-60764 (URN)10.1007/s11854-010-0005-4 (DOI)000283488000005 ()
Note
Tidigare titel: The Dirichlet problem in Lipschitz domains with boundary data in Besov spaces for higher order elliptic systems with rough coefficients Available from: 2010-10-26 Created: 2010-10-26 Last updated: 2010-12-16
Maz'ya, V. & Shaposhnikova, T. (2009). A collection of sharp dilation invariant integral inequalities for differentiable functions (vol. 8ed.). In: Vladimir Maz'ya (Ed.), Sobolev spaces in mathematics. I (pp. 223-247). Springer
Open this publication in new window or tab >>A collection of sharp dilation invariant integral inequalities for differentiable functions
2009 (English)In: Sobolev spaces in mathematics. I / [ed] Vladimir Maz'ya, Springer , 2009, vol. 8, p. 223-247Chapter in book (Other (popular science, discussion, etc.))
Place, publisher, year, edition, pages
Springer, 2009 Edition: vol. 8
Series
International Mathematical Series (New York) ; 8
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52038 (URN)978-0-387-85647-6 (ISBN)
Available from: 2009-11-30 Created: 2009-11-30 Last updated: 2010-11-12
Shaposhnikova, T. (2009). Description of Pointwise Multipliers in Pairs of Besov Spaces B-1(k)(R-n). ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 28(1), 67-85
Open this publication in new window or tab >>Description of Pointwise Multipliers in Pairs of Besov Spaces B-1(k)(R-n)
2009 (English)In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, ISSN 0232-2064, Vol. 28, no 1, p. 67-85Article in journal (Refereed) Published
Abstract [en]

Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space B-1(m)(R-n) into the Besov space B-1(l)(R-n) with integer l and m, 0 < l <= m, are found. It is shown that multipliers between B-1(m)(R-n) and B-1(l)(R-n) form the space of traces of multipliers between the Sobolev classes W-1(m+1)(R-+(n+1)) and W-1(l+1)(R-+(n+1)).

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-16714 (URN)10.4171/ZAA/1373 (DOI)
Available from: 2009-02-14 Created: 2009-02-13 Last updated: 2014-09-15
Shaposhnikova, T. (2009). Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary. Paper presented at Seventh ISAAC Congress.
Open this publication in new window or tab >>Dirichlet problem for higher order elliptic systems with BMO assumptions on the coefficients and the boundary
2009 (English)Conference paper, Published paper (Refereed)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52047 (URN)
Conference
Seventh ISAAC Congress
Available from: 2009-11-30 Created: 2009-11-30 Last updated: 2010-11-12
Shaposhnikova, T. (2009). Higher regularity in the classical layer potential theory for Lipschitz domains. Paper presented at Advances in boundary integral equations and related topics. A conference in honor of G.C. Hsiao's 75th borthday.
Open this publication in new window or tab >>Higher regularity in the classical layer potential theory for Lipschitz domains
2009 (English)Conference paper, Published paper (Refereed)
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52046 (URN)
Conference
Advances in boundary integral equations and related topics. A conference in honor of G.C. Hsiao's 75th borthday
Available from: 2009-11-30 Created: 2009-11-30 Last updated: 2010-11-12
Maz´ya, V., Mitrea, M. & Shaposhnikova, T. (2009). The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 43(3), 217-235
Open this publication in new window or tab >>The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO
2009 (English)In: FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, ISSN 0016-2663, Vol. 43, no 3, p. 217-235Article in journal (Refereed) Published
Abstract [en]

The goal of this work is to study the inhomogeneous Dirichlet problem for the Stokes system in a Lipschitz domain Omega aS dagger a"e (n) , na (c) 3/42. Our main result is that this problem is well posed in Besov-Triebel-Lizorkin spaces, provided that the unit normal nu to Omega has small mean oscillation.

Keywords
Stokes system, Lipschitz domain, boundary value problem, Besov-Triebel-Lizorkin spaces
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-21519 (URN)10.1007/s10688-009-0029-7 (DOI)
Available from: 2009-10-02 Created: 2009-10-02 Last updated: 2010-11-12
Shaposhnikova, T. (2009). Von Neumann with the Devil, a play by Lars Gårding, translated into Russian by T. Shaposhnikova. Algebra i Analiz, 21(5), 222-226
Open this publication in new window or tab >>Von Neumann with the Devil, a play by Lars Gårding, translated into Russian by T. Shaposhnikova
2009 (Russian)In: Algebra i Analiz, Vol. 21, no 5, p. 222-226Article in journal (Refereed) Published
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52486 (URN)
Available from: 2009-12-23 Created: 2009-12-23 Last updated: 2010-11-12
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