We prove that manifold constrained p(x)-harmonic maps are locally C1,β0-regular outside a set of zero n-dimensional Lebesgue’s measure, for some β∈ (0 , 1). We also provide an estimate from above of the Hausdorff dimension of the singular set.
Partial regularity for manifold constrained p(x)-harmonic maps
De Filippis C.
2019-01-01
Abstract
We prove that manifold constrained p(x)-harmonic maps are locally C1,β0-regular outside a set of zero n-dimensional Lebesgue’s measure, for some β∈ (0 , 1). We also provide an estimate from above of the Hausdorff dimension of the singular set.
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