On improved estimates for parabolic equations with double degeneracy
Tóm tắt
We obtain improved pointwise estimates for solutions to nonlinear parabolic equations with double degeneracy. These estimates differ from the classical estimates known for the linear case in that the supremum of the modulus of a solution is estimated by the sum of two powers of the integral norm of the solution.
Tài liệu tham khảo
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasi-linear Equations of Parabolic Type (Nauka, Moscow, 1967; Am. Math. Soc., Providence, RI, 1968), Transl. Math. Monogr. 23.
E. DiBenedetto, Degenerate Parabolic Equations (Springer, New York, 1993).
M. M. Porzio, “L ∞loc -Estimates for Degenerate and Singular Parabolic Equations,” Nonlinear Anal., Theory Methods Appl. 17(11), 1093–1107 (1991).