L.A.M. Fattorusso | Boundedness of the solutions to a kind of parabolic systems
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 01/08/2022

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Luisa A. M. Fattorusso (Infrastructure and Sustainable Energy, Mediterranea University of Reggio Calabria) 
Boundedness of the solutions to a kind of parabolic systems

We deal with nonlinear systems of parabolic type satisfying componentwise
structural conditions. The nonlinear terms are Carath´eodory maps having controlled growth with respect to the solution and the gradient and the data are in anisotropic Lebesgue spaces. Under these assumptions we obtain essential boundedness of the weak solutions.
References
[1] O.A. Ladyzhenskaya, V.A. Solonnikov, N.N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Translations of Math. Mon., Vol. 23,
Amer. Math. Soc.
[2] F. Leonetti, P.V. Petricca, Regularity for solutions to some nonlinear elliptic systems, Complex Var. Elliptic Eq. 12 (2011), 1099-1113.
[3] S.-S. Byun, D.K. Palagachev, P. Shin, Boundedness of solutions to quasilinear parabolic equations, J. Differential Equations 261 (2016), 6790-6805.
[4] D.K. Palagachev, L.G. Softova, Boundedness of solutions to a class of coercive systems with Morrey data, Nonlinear Anal. (2020), 16 p.
[5] L.G. Softova, Boundedness of the solutions to nonlinear systems with Morrey data, Complex Var. Elliptic Equ., 63 (2018)