Gradient continuity (C¹-regularity) for p-Laplacian obstacle problems is established under Dini mean oscillation conditions on coefficients, source term, and obstacle, weakening classical Dini continuity assumptions.
ANTONINI, Local and globalC 1,β-regularity for uniformly elliptic quasilinear equations of p-Laplace and Orlicz-Laplace type.Preprint
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Existence and C^{1,α} regularity are established for solutions of the obstacle p-Laplacian problem with singular discontinuous reaction.
The paper establishes an anisotropic Struwe decomposition with bubble interaction estimates, a short classification proof, and quantitative stability for perturbations of the anisotropic critical p-Laplace equation.
Uniqueness of weak solutions is established and necessary and sufficient conditions for existence are provided for singular anisotropic quasilinear elliptic problems with p-sublinear perturbations.
citing papers explorer
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Gradient continuity for $p$-Laplacian obstacle problems under mean oscillation conditions
Gradient continuity (C¹-regularity) for p-Laplacian obstacle problems is established under Dini mean oscillation conditions on coefficients, source term, and obstacle, weakening classical Dini continuity assumptions.
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The obstacle problem for singular quasi-linear elliptic equations
Existence and C^{1,α} regularity are established for solutions of the obstacle p-Laplacian problem with singular discontinuous reaction.
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On the anisotropic critical $p$-Laplace equation: classification, decomposition, and stability results
The paper establishes an anisotropic Struwe decomposition with bubble interaction estimates, a short classification proof, and quantitative stability for perturbations of the anisotropic critical p-Laplace equation.
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Existence and uniqueness of weak solutions to singular anisotropic elliptic problems
Uniqueness of weak solutions is established and necessary and sufficient conditions for existence are provided for singular anisotropic quasilinear elliptic problems with p-sublinear perturbations.