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Higher Integrability of the Gradient in Degenerate Elliptic Equations

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Abstract

We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta–Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Hölder continuity result for the weak solution.

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  1. Institut Elie Cartan, Université Henri Poincaré Nancy 1, B.P. 239, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    Pierre Dreyfuss

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  1. Pierre Dreyfuss
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Dreyfuss, P. Higher Integrability of the Gradient in Degenerate Elliptic Equations. Potential Anal 26, 101–119 (2007). https://doi.org/10.1007/s11118-006-9030-4

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