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On the boundary conditions in estimating by div and curl
Gyula Csató, Olivier Kneuss, Dhanya Rajendran
In this paper we study under what boundary conditions the inequality $$\|\nablaω\|_{L^2(Ω)}^2\leq C\left(\|{\rm curl}ω\|_{L^2(Ω)}^2+ \|{\rm div}ω\|_{L^2(Ω)}^2+\|ω\|_{L^2(Ω)}^2\righ…
Flows generated by divergence free vector fields with compact support
Olivier Kneuss, Wladimir Neves
We are concerned with the theory of existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fiel…
Bi-Sobolev Solutions to the Prescribed Jacobian Inequality in the Plane with Data
Julian Fischer, Olivier Kneuss
We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function with , i.e. bi-Sobolev solutions for the prescribed…
Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models
Lawrence C. Evans, Olivier Kneuss, Hung Tran
We study the partial regularity of minimizers for certain singular functionals in the calculus of variations, motivated by Ball and Majumdar's recent modification [BM] of the Landa…