Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems

By Andrea Cianchi, Vladimir G. Maz'ya. 2012

154 citations recorded by the source corpus.

Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bbb1aa03a82c39110b2f547e0e4d2fe9d5bacd37

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems (2017, background): “1) satisfies ellipticity and monotonicity conditions, not necessarily of power type [21,22].”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, background): “tes for boundary value POINTWISE CALDERON-ZYGMUND GRADIENT ESTIMATES FOR THE´ p-LAPLACE SYSTEM 3 problems, under minimal regularity assumptions on the boundary of the ground domain, are the object of [2, 5, 15, 16, 51, 41, 42]. Our main results show that, as in the linear case ∇u and F are linked th”
Lipschitz Bounds and Nonautonomous Integrals (2020, methodology): “ollaries of the main results, but Theorem 3. This in fact requires some additional arguments to reach the = borderline case in the ﬁrst bound from (1.19), thereby reconnecting to the known literature [2,19,20] in the case f≡ 0. Section 11 contains applications to obstacle problems. Finally, Section ”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “We refer for other results on existence and gradient estimates to [10, 12, 60, 160, 44, 59, 61], nonexistence [95, 126], regularity [143, 144, 58] and then [37, 73], and foundations of the potential theory to [19].”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, background): “Everywhere Lipschitz continuity up to the boundary for either the Dirichlet or the Neumann problem has been recently considered by Cianchi and Maz’ya [5] under uniformly elliptic conditions.”