Solutions to p-Laplace equations are not, in general, of class C2. The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz’ya shows that, if the source term is in L2, then the field |∇u|p-2∇u is in W1,2. The L2-regularity of the source term is also a necessary condition. Here, under suitable assumptions, we obtain sharp second order estimates, thus proving the optimal regularity of the vector field |∇u|p-2∇u, up to the boundary.
Optimal second order boundary regularity for solutions to p-Laplace equations
Montoro L.;Muglia L.;Sciunzi B.
2025-01-01
Abstract
Solutions to p-Laplace equations are not, in general, of class C2. The study of Sobolev regularity of the second derivatives is, therefore, a crucial issue. An important contribution by Cianchi and Maz’ya shows that, if the source term is in L2, then the field |∇u|p-2∇u is in W1,2. The L2-regularity of the source term is also a necessary condition. Here, under suitable assumptions, we obtain sharp second order estimates, thus proving the optimal regularity of the vector field |∇u|p-2∇u, up to the boundary.File in questo prodotto:
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