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Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations. / Tersenov, Alkis S.; Tersenov, Aris S.

In: Journal of Functional Analysis, Vol. 272, No. 10, 15.05.2017, p. 3965-3986.

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

Harvard

Tersenov, AS & Tersenov, AS 2017, 'Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations', Journal of Functional Analysis, vol. 272, no. 10, pp. 3965-3986. https://doi.org/10.1016/j.jfa.2017.02.014

APA

Tersenov, A. S., & Tersenov, A. S. (2017). Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations. Journal of Functional Analysis, 272(10), 3965-3986. https://doi.org/10.1016/j.jfa.2017.02.014

Vancouver

Tersenov AS, Tersenov AS. Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations. Journal of Functional Analysis. 2017 May 15;272(10):3965-3986. doi: 10.1016/j.jfa.2017.02.014

Author

Tersenov, Alkis S. ; Tersenov, Aris S. / Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations. In: Journal of Functional Analysis. 2017 ; Vol. 272, No. 10. pp. 3965-3986.

BibTeX

@article{af2328ef0182408cb46c74e7f2506951,
title = "Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations",
abstract = "The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative ut of a solution u belongs to L∞ under a suitable assumption on the smoothness of the initial data. Moreover, if the domain satisfies some additional geometric restrictions, then the spatial derivatives uxi belong to L∞ as well. In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.",
keywords = "Degenerate parabolic equations, Singular parabolic equations, DEGENERATE, ULTRAPARABOLIC EQUATION",
author = "Tersenov, {Alkis S.} and Tersenov, {Aris S.}",
year = "2017",
month = may,
day = "15",
doi = "10.1016/j.jfa.2017.02.014",
language = "English",
volume = "272",
pages = "3965--3986",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "10",

}

RIS

TY - JOUR

T1 - Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations

AU - Tersenov, Alkis S.

AU - Tersenov, Aris S.

PY - 2017/5/15

Y1 - 2017/5/15

N2 - The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative ut of a solution u belongs to L∞ under a suitable assumption on the smoothness of the initial data. Moreover, if the domain satisfies some additional geometric restrictions, then the spatial derivatives uxi belong to L∞ as well. In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.

AB - The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative ut of a solution u belongs to L∞ under a suitable assumption on the smoothness of the initial data. Moreover, if the domain satisfies some additional geometric restrictions, then the spatial derivatives uxi belong to L∞ as well. In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.

KW - Degenerate parabolic equations

KW - Singular parabolic equations

KW - DEGENERATE

KW - ULTRAPARABOLIC EQUATION

UR - http://www.scopus.com/inward/record.url?scp=85014569275&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2017.02.014

DO - 10.1016/j.jfa.2017.02.014

M3 - Article

AN - SCOPUS:85014569275

VL - 272

SP - 3965

EP - 3986

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 10

ER -

ID: 10277211