Higher regularity for solutions to elliptic systems in divergence form subject to mixed boundary conditions

On the C regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients

We prove C1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients. This note addresses a question raised to the author by Haim Brezis, in connection with his solution of a conjecture of Serrin concerning divergence form second order elliptic equations (see [1] and [2]). If the coefficients of the equations (or systems) are Hölder continuous, then H1 solut...

Boundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems

for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality...

Boundary regularity result for quasilinear elliptic systems

* Correspondence: shiny0320@163. com Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian, China Full list of author information is available at the end of the article Abstract We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under controllable growth condition, and obtain a general criterion for ...

Finding Multiple Solutions to Elliptic PDE with Nonlinear Boundary Conditions

In this paper, in order to solve an elliptic partial differential equation with a nonlinear boundary condition for multiple solutions, the authors combine a minimax approach with a boundary integral-boundary element method, and identify a subspace and its special expression so that all numerical computation and analysis can be carried out more efficiently based on information of functions only ...

Fractional Order Diierentiability of the Gradient of Solutions to Elliptic Equations with Mixed Boundary Conditions