We establish sharp global regularity results for solutions to nonhomogeneous, nonuniformly elliptic systems with zero boundary conditions imposed only on some part of the boundary of convex domains. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the forcing term, thus positively settling the optimality issue raised in [11].
Borderline Global Regularity for Nonuniformly Elliptic Systems
Piccinini, Mirco
2023-01-01
Abstract
We establish sharp global regularity results for solutions to nonhomogeneous, nonuniformly elliptic systems with zero boundary conditions imposed only on some part of the boundary of convex domains. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the forcing term, thus positively settling the optimality issue raised in [11].File in questo prodotto:
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