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Time derivative estimates for parabolic $p$-Laplace equations and applications to optimal regularity
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abstract
We establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximation method. As a consequence, we obtain an optimal regularity result with a connection to the well-known $C^{p'}$-conjecture in the elliptic setting. Finally, we extend our method to treat global regularity results for both fully nonlinear and general quasilinear degenerate parabolic problems.
Forward citations
Cited by 2 Pith papers
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Harnack inequality for degenerate fully nonlinear parabolic equations
An intrinsic Harnack inequality, with two distinct waiting times, is proven for nonnegative viscosity solutions of degenerate fully nonlinear parabolic equations, yielding local Holder continuity.
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Boundary H\"older gradient estimates for parabolic $p$-Laplace type equations
This paper establishes boundary pointwise and global C^{1,α} gradient estimates for viscosity solutions of parabolic p-Laplace type equations with general boundary data.
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