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University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Higher gradient integrability for $\sigma$-harmonic maps in dimension two

## Higher gradient integrability for $\sigma$-harmonic maps in dimension twoAdd to your list(s) Download to your calendar using vCal - Dr. Mariapia Palombaro, University of Sussex
- Monday 06 October 2014, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact Harsha Hutridurga. I will present some recent results concerning the higher gradient integrability of $\sigma$-harmonic functions $u$ with discontinuous coefficients $\sigma$ i.e., weak solutions of $\nabla\cdot(\sigma\nabla u) = 0$. When $\sigma$ is assumed to be symmetric, then the optimal integrability exponent of the gradient field is known
thanks to the work of Astala and Leonetti and Nesi. I will discuss the case when only the ellipticity is fixed and $\sigma$ is otherwise unconstrained and show that the optimal exponent is attained on the class of two-phase conductivities $\sigma : \Omega\subset\mathbb{R} (Joint work with V. Nesi and M. Ponsiglione.) This talk is part of the Geometric Analysis and Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
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