Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials-Reference-Cited by-同舟云学术

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Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials

Published:2019-03-25 Issue:1 Volume:16 Page:28-45
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Buryachenko Kateryna¹

Affiliation:

1. Vasyl' Stus Donetsk National University, Vinnytsia, Ukraine

Abstract

For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Reference23 articles.

1. Bogelein, V., Duzaar, F. & Marcellini, P. (2013). Parabolic equations with p, q− growth. J. Math. Pures Appl., 100, рр. 535-563.

2. Bogelein, V., Duzaar, F., & Gianazza, U. (2013). Porous medium type equations with measure data and potential estimates. SIAM J. Math. Anal., 45, рр. 3283-3330.

3. Buryachenko, K. O. & Skrypnik, I. I. (2017). Pointwise estimates of solutions to the double-phase elliptic equations. J. Math. Sci., 222, рр. 772-786.

4. Buryachenko, K. O. & Skrypnik, I. I. (2019). Riesz potentials and pointwise estimates of solutions to anisotropic porous medium equation. Nonlin. Analysis, 178, рр. 56-85.

5. DiBenedetto, E. (1993). Degenerate Parabolic Equations. New York: Springer.

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