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On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition. / Arkhipova, A. A.

In: Journal of Mathematical Sciences , Vol. 87, No. 2, 01.01.1997, p. 3284-3303.

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

Harvard

Arkhipova, AA 1997, 'On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition', Journal of Mathematical Sciences , vol. 87, no. 2, pp. 3284-3303. https://doi.org/10.1007/BF02355581

APA

Arkhipova, A. A. (1997). On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition. Journal of Mathematical Sciences , 87(2), 3284-3303. https://doi.org/10.1007/BF02355581

Vancouver

Arkhipova AA. On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition. Journal of Mathematical Sciences . 1997 Jan 1;87(2):3284-3303. https://doi.org/10.1007/BF02355581

Author

Arkhipova, A. A. / On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition. In: Journal of Mathematical Sciences . 1997 ; Vol. 87, No. 2. pp. 3284-3303.

BibTeX

@article{ca3b4f83b5254b5b923310409208418d,
title = "On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition",
abstract = "Properties of generalized solutions of model nonlinear elliptic systems of second order are studied in the semiball B1+ = B 1(0)∩{xn > 0} ⊂ ℝn, with the oblique derivative type boundary condition on Γ1 = B 1(0)∩{xn = 0}. For solutions u ∈ H 1(B1+) of systems of the form d/dx α aαk(ux) = 0, k ≤ N, it is proved that the derivatives ux are H{\"o}lder in B 1+ ∪ Γ1)\∑, where H n-p(∑) = 0, p > 2. It is shown for continuous solutions u from H1 (B1+) of systems d/dxα aαk (u,ux) = 0 that the derivatives ux are H{\"o}lder on the set (B1+ ∪Γ1)\∑, dimH ∑ ≤ n - 2.",
author = "Arkhipova, {A. A.}",
year = "1997",
month = jan,
day = "1",
doi = "10.1007/BF02355581",
language = "English",
volume = "87",
pages = "3284--3303",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - On the regularity of solutions of model nonlinear elliptic systems with the oblique derivative type boundary condition

AU - Arkhipova, A. A.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Properties of generalized solutions of model nonlinear elliptic systems of second order are studied in the semiball B1+ = B 1(0)∩{xn > 0} ⊂ ℝn, with the oblique derivative type boundary condition on Γ1 = B 1(0)∩{xn = 0}. For solutions u ∈ H 1(B1+) of systems of the form d/dx α aαk(ux) = 0, k ≤ N, it is proved that the derivatives ux are Hölder in B 1+ ∪ Γ1)\∑, where H n-p(∑) = 0, p > 2. It is shown for continuous solutions u from H1 (B1+) of systems d/dxα aαk (u,ux) = 0 that the derivatives ux are Hölder on the set (B1+ ∪Γ1)\∑, dimH ∑ ≤ n - 2.

AB - Properties of generalized solutions of model nonlinear elliptic systems of second order are studied in the semiball B1+ = B 1(0)∩{xn > 0} ⊂ ℝn, with the oblique derivative type boundary condition on Γ1 = B 1(0)∩{xn = 0}. For solutions u ∈ H 1(B1+) of systems of the form d/dx α aαk(ux) = 0, k ≤ N, it is proved that the derivatives ux are Hölder in B 1+ ∪ Γ1)\∑, where H n-p(∑) = 0, p > 2. It is shown for continuous solutions u from H1 (B1+) of systems d/dxα aαk (u,ux) = 0 that the derivatives ux are Hölder on the set (B1+ ∪Γ1)\∑, dimH ∑ ≤ n - 2.

UR - http://www.scopus.com/inward/record.url?scp=53249115559&partnerID=8YFLogxK

U2 - 10.1007/BF02355581

DO - 10.1007/BF02355581

M3 - Article

AN - SCOPUS:53249115559

VL - 87

SP - 3284

EP - 3303

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 51918387