Gradient regularity via rearrangements for p-Laplacian type elliptic boundary value problems

• A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.

Nyckelord

Nonlinear elliptic equations; Dirichlet problems; Neumann problems; gradient estimates; rearrangements; Lorentz spaces; Orlicz spaces

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MATEMATIK

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