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SUMMARY:Higher gradient integrability for σ-harmonic maps in dimension tw
 o - Mariapia Palombaro (University of Sussex)
DTSTART:20141006T140000Z
DTEND:20141006T150000Z
UID:TALK54958@talks.cam.ac.uk
CONTACT:Amit Einav
DESCRIPTION:I will present some recent results concerning the higher gradi
 ent inte- grability of σ-harmonic functions u with discontinuous coeffici
 ents σ\, i.e. weak solutions of div(σ∇u) = 0. When σ is assumed to be
  symmetric\, then the optimal integrability exponent of the gradient field
  is known thanks to the work of Astala and Leonetti & Nesi. I will discuss
  the case when only the ellipticity is fixed and σ is otherwise unconstra
 ined and show that the optimal exponent is attained on the class of two-ph
 ase conductivities σ:Ω⊂R2 →(σ1\,σ2)⊂M2×2. The optimal exponent 
 is established\, in the strongest possible way of the existence of so-call
 ed exact solutions\, via the exhibition of optimal microgeometries.\n(Join
 t work with V. Nesi and M. Ponsiglione.)
LOCATION:CMS\, MR13
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