NONSTATIONARY VENTTSEL PROBLEM WITH VMOx LEADING COEFFICIENTS

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详细

We obtain some new results on strong solvability in the Sobolev spaces of the linear Venttsel initial-boundary value problems to parabolic equations with discontinuous leading coefficients.

作者简介

D. Apushkinskaya

St. Petersburg Department of V.A. Steklov Mathematical Institute; Peoples’ Friendship University of Russia (RUDN University)

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Email: apushkinskaya@gmail.com
Russian Federation, St. Petersburg; Russian Federation, Moscow

A. Nazarov

St. Petersburg Department of V.A. Steklov Mathematical Institute; St. Petersburg State University

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Email: al.il.nazarov@gmail.com
Russian Federation, St. Petersburg; Russian Federation, St. Petersburg

D. Palagachev

Polytechnic University of Bari

编辑信件的主要联系方式.
Email: dian.palagachev@poliba.it
Italy, Bari

L. Softova

University of Salerno

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Email: lsoftova@unisa.it
Italy, Fisciano

参考

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  2. Apushkinskaya D.E., Nazarov A.I. A survey of results on nonlinear Venttsel problems // Appl. Math. 2000. V. 45. № 1. P. 69–80.
  3. Apushkinskaya D.E., Nazarov A.I., Palagachev D.K., Softova L.G. Venttsel boundary value problems with discontinuous data // SIAM J. Math. Anal. 2021. V. 53. № 1. P. 221–252.
  4. Chiarenza F., Frasca M., Longo P. W2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients // Trans. Amer. Math. Soc. 1993. V. 336. № 2. P. 841–853.
  5. Maugeri A., Palagachev D.K., Softova L.G. Elliptic and parabolic equations with discontinuous coefficients, volume 109 of Mathematical Research. Wiley-VCH Verlag Berlin GmbH, Berlin, 2000.
  6. Krylov N.V. Lectures on elliptic and parabolic equations in Sobolev spaces, volume 96 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008.
  7. Dong H., Kim D. On the Lp-solvability of higher order parabolic and elliptic systems with BMO coefficients // Arch. Ration. Mech. Anal. 2011. V. 199. № 3. P. 889–941.
  8. Апушкинская Д.Е., Назаров А.И. Начально-краевая задача с граничным условием Вентцеля для недивергентных параболических уравнений // Алгебра и анализ. 1994. Т. 6. № 6. С. 1–29.
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  11. Бесов О.В., Ильин В.П., Никольский С.М. Интегральные представления функций и теоремы вложения. Наука, М., 1996. 2-е изд., перераб. и доп.
  12. Krylov N.V. On parabolic Adams’s, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces // Math. Eng. 2023. V. 5. № 2. P. 1–20.

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