Borderline Global Regularity for Nonuniformly Elliptic Systems
Cristiana De Filippis, Mirco Piccinini
Abstract
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].
Topics & Concepts
MathematicsForcing (mathematics)Lipschitz continuityRegular polygonBoundary (topology)Mathematical analysisTerm (time)Lorentz transformationBoundary value problemGeometryClassical mechanicsQuantum mechanicsPhysicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems