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REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD. / Arkhipova, Arina A.; Stara, Jana.

In: Topological Methods in Nonlinear Analysis, Vol. 52, No. 1, 09.2018, p. 111-146.

Research output: Contribution to journal › Article › peer-review

Harvard

Arkhipova, AA & Stara, J 2018, 'REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD', Topological Methods in Nonlinear Analysis, vol. 52, no. 1, pp. 111-146. https://doi.org/10.12775/TMNA.2018.006

APA

Arkhipova, A. A., & Stara, J. (2018). REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD. Topological Methods in Nonlinear Analysis, 52(1), 111-146. https://doi.org/10.12775/TMNA.2018.006

Vancouver

Arkhipova AA, Stara J. REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD. Topological Methods in Nonlinear Analysis. 2018 Sep;52(1):111-146. https://doi.org/10.12775/TMNA.2018.006

Author

Arkhipova, Arina A. ; Stara, Jana. / REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD. In: Topological Methods in Nonlinear Analysis. 2018 ; Vol. 52, No. 1. pp. 111-146.

BibTeX

@article{fc44cc87b75c45c69f2b509f0dec77e2,
title = "REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD",
abstract = "Partial regularity of solutions to a class of 2m-order quasilinear parabolic systems and full interior regularity for 2m-order linear parabolic systems with non smooth in time principal matrices is proved in the paper. The coefficients are assumed to be bounded and measurable in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the (A(t), m)-caloric approximation method, m >= 1. It is both an extension of the A(t)-caloric approximation applied by the authors earlier to study regularity problem for systems of the second order with non-smooth coefficients and an extension of the A-polycaloric lemma proved by V. Bogelein in [6] to systems of 2m-order.",
keywords = "High order parabolic systems, regularity problem, ELLIPTIC-SYSTEMS, VMO COEFFICIENTS, WEAK SOLUTIONS, SINGULAR SETS, NONSMOOTH, EQUATIONS, Regularity problem",
author = "Arkhipova, {Arina A.} and Jana Stara",
year = "2018",
month = sep,
doi = "10.12775/TMNA.2018.006",
language = "Английский",
volume = "52",
pages = "111--146",
journal = "Topological Methods in Nonlinear Analysis",
issn = "1230-3429",
publisher = "Wydawnictwo Uniwersytetu Miko{\l}aja Kopernika",
number = "1",

}

RIS

TY - JOUR

T1 - REGULARITY PROBLEM FOR 2m-ORDER QUASILINEAR PARABOLIC SYSTEMS WITH NON SMOOTH IN TIME PRINCIPAL MATRIX. (A(t), m)-CALORIC APPROXIMATION METHOD

AU - Arkhipova, Arina A.

AU - Stara, Jana

PY - 2018/9

Y1 - 2018/9

N2 - Partial regularity of solutions to a class of 2m-order quasilinear parabolic systems and full interior regularity for 2m-order linear parabolic systems with non smooth in time principal matrices is proved in the paper. The coefficients are assumed to be bounded and measurable in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the (A(t), m)-caloric approximation method, m >= 1. It is both an extension of the A(t)-caloric approximation applied by the authors earlier to study regularity problem for systems of the second order with non-smooth coefficients and an extension of the A-polycaloric lemma proved by V. Bogelein in [6] to systems of 2m-order.

AB - Partial regularity of solutions to a class of 2m-order quasilinear parabolic systems and full interior regularity for 2m-order linear parabolic systems with non smooth in time principal matrices is proved in the paper. The coefficients are assumed to be bounded and measurable in the time variable and VMO-smooth in the space variables uniformly with respect to time. To prove the result, we apply the (A(t), m)-caloric approximation method, m >= 1. It is both an extension of the A(t)-caloric approximation applied by the authors earlier to study regularity problem for systems of the second order with non-smooth coefficients and an extension of the A-polycaloric lemma proved by V. Bogelein in [6] to systems of 2m-order.

KW - High order parabolic systems

KW - regularity problem

KW - ELLIPTIC-SYSTEMS

KW - VMO COEFFICIENTS

KW - WEAK SOLUTIONS

KW - SINGULAR SETS

KW - NONSMOOTH

KW - EQUATIONS

KW - Regularity problem

UR - http://www.scopus.com/inward/record.url?scp=85055143663&partnerID=8YFLogxK

U2 - 10.12775/TMNA.2018.006

DO - 10.12775/TMNA.2018.006

M3 - статья

VL - 52

SP - 111

EP - 146

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

SN - 1230-3429

IS - 1

ER -

ID: 30165596