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Improved estimates for parabolic \(p\)-Laplace type equations. (English. Russian original) Zbl 1334.35172

J. Math. Sci., New York 210, No. 4, 429-457 (2015); translation from Probl. Mat. Anal. 81, 81-106 (2015).
The author considers nonlinear parabolic \(p\)-Laplace type equations and obtains estimates improving similar estimates in the celebrated monograph by E. DiBenedetto. Thanks to these estimates, the author gets local “entropy” estimates for the gradients of sign-variable solutions. The author uses the entropy estimates to prove the existence of the Cauchy problem in the entire space with sign-variable initial data.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35B65 Smoothness and regularity of solutions to PDEs
35K55 Nonlinear parabolic equations
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