Second-order differentiability for solutions of elliptic equations in the plane

Vladimir Maz'ya; Robert McOwen

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arXiv · 1303.3254

Second-order differentiability for solutions of elliptic equations in the plane

Vladimir Maz'ya·Robert McOwen

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Abstract

For a second-order elliptic equation of nondivergence form in the plane, we investigate conditions on the coefficients which imply that all strong solutions have first-order derivatives that are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of continuity satisfying the square-Dini condition, and obtain additional conditions associated with a dynamical system that is derived from the coefficients of the elliptic equation. Our results extend those of previous authors who assume the modulus of continuity satisfies the Dini condition.

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Vladimir Maz'ya, Robert McOwen. 2013-03-13. Second-order differentiability for solutions of elliptic equations in the plane. https://arxiv.org/abs/1303.3254

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