Weak differentiability to nonuniform nonlinear degenerate elliptic systems under p,q-growth condition on the Heisenberg group

Differentiability of Solutions for the Non-degenerate P-laplacian in the Heisenberg Group

We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.

Boundary regularity for elliptic systems under a natural growth condition

We consider weak solutions u ∈ u0 +W 1,2 0 (Ω,R )∩L∞(Ω,RN ) of second order nonlinear elliptic systems of the type −div a( · , u,Du) = b( · , u,Du) in Ω with an inhomogeneity obeying a natural growth condition. In dimensions n ∈ {2, 3, 4} we show that Hn−1-almost every boundary point is a regular point for Du, provided that the boundary data and the coefficients are sufficiently smooth. Mathema...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Degenerate Nonlinear Programming with a Quadratic Growth Condition

We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualiication imply that local minima of nonlinear programs are isolated stationary points. As a result, when started suuciently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an ...

Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case 1<m<2 under Natural Growth Condition

where Ω is a bounded domain in R, u and Bi taking values in R , and Aαi ·, ·, · has value in R . N > 1, u : Ω → RDu {Dαu}, 1 ≤ α ≤ n, 1 ≤ i ≤ N stand for the div of u and 1 < m < 2. To define weak solution to 1.1 , one needs to impose certain structural and regularity conditions on Aαi and the inhomogeneity Bi, as well as to restrict u to a particular class of functions as follows, for 1 < m < ...