The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 93-99.

Voir la notice de l'article provenant de la source Math-Net.Ru

New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel' problem for parabolic equations with discontinuous leading coefficients are obtained.
Keywords: quasilinear second-order parabolic equation, Venttsel' problem, $VMO_x$ class, a priori estimate, existence theorem.
@article{FAA_2023_57_2_a5,
     author = {D. E. Apushkinskaya and A. I. Nazarov and D. K. Palagachev and L. G. Softova},
     title = {The quasilinear parabolic {Venttsel'} problem with discontinuous leading coefficients},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {93--99},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a5/}
}
TY  - JOUR
AU  - D. E. Apushkinskaya
AU  - A. I. Nazarov
AU  - D. K. Palagachev
AU  - L. G. Softova
TI  - The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2023
SP  - 93
EP  - 99
VL  - 57
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a5/
LA  - ru
ID  - FAA_2023_57_2_a5
ER  - 
%0 Journal Article
%A D. E. Apushkinskaya
%A A. I. Nazarov
%A D. K. Palagachev
%A L. G. Softova
%T The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2023
%P 93-99
%V 57
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a5/
%G ru
%F FAA_2023_57_2_a5
D. E. Apushkinskaya; A. I. Nazarov; D. K. Palagachev; L. G. Softova. The quasilinear parabolic Venttsel' problem with discontinuous leading coefficients. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 93-99. http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a5/

[1] A. D. Venttsel, Teoriya veroyatn. i ee primen., 4:2 (1959), 172–185

[2] D. E. Apushkinskaya, A. I. Nazarov, Appl. Math., 45:1 (2000), 69–80 | DOI | MR | Zbl

[3] D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova, SIAM J. Math. Anal., 53:1 (2021), 221–252 | DOI | MR | Zbl

[4] D. E. Apushkinskaya, A. I. Nazarov, Algebra i analiz, 6:6 (1994), 1–29

[5] D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova, Dokl. RAN, 10:2 (2023)

[6] L. G. Softova, Nonlinear Anal., 52:4 (2003), 1079–1093 | DOI | MR | Zbl

[7] N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, Graduate Studies in Math., vol. 96, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[8] A. Maugeri, D. K. Palagachev, L. G. Softova, Elliptic and Parabolic Equations with Discontinuous Coefficients, Math. Research. 109, Wiley-VCH Verlag Berlin GmbH, Berlin, 2000 | MR | Zbl

[9] H. Amann, M. G. Crandall, Indiana Univ. Math. J., 27:5 (1978), 779–790 | DOI | MR | Zbl

[10] D. E. Apushkinskaya, A. I. Nazarov, Nonlinear Evolution Equations, Amer. Math. Soc. Translations Ser. 2, 164, Amer. Math. Soc., Providence, RI, 1995, 1–13 | DOI | MR | Zbl

[11] V. A. Solonnikov, Zap. nauchn. sem. LOMI, 27, 1972, 194–210 | Zbl