We study the regularity properties of solutions to the non-homogeneous singular p(x)-Laplacian system in a bounded domain of Rn. Under suitable restrictions on the range of p(x), we construct a W2,r solution, with r>n, that implies the Hölder continuity of the gradient. Moreover, assuming just p(x)∈(1,2) we prove that the second derivatives belong to L2.
High regularity of the solution to the singular elliptic p(⋅)-Laplacian system
Crispo F;
2020
Abstract
We study the regularity properties of solutions to the non-homogeneous singular p(x)-Laplacian system in a bounded domain of Rn. Under suitable restrictions on the range of p(x), we construct a W2,r solution, with r>n, that implies the Hölder continuity of the gradient. Moreover, assuming just p(x)∈(1,2) we prove that the second derivatives belong to L2.File in questo prodotto:
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