Albert Clop

Beltrami equations with coefficient in the Sobolev space W1,p

We study the removable singularities for solutions to the Beltrami equation Əƒ = μ Əƒ, where μ is a bounded function, ||μ|| ∞ ≤ k-1/k+1 < 1, and such that μ ∈ W1,p for some p ≤ 2. Our results are based on an extended version of the well known Weyl’s lemma, asserting that distributional solutions are actually true solutions. Our main result is that quasiconformal mappings with compactly supported Beltrami coefficient μ ∈ W1,p, 2k2/k2+1 < p ≤ 2, preserve compact sets of σ-finite length and vanishing analytic capacity, even though they need not be bilipschitz.

Fractional Differentiability for Solutions of Nonlinear Elliptic Equations

AbstractWe study nonlinear elliptic equations in divergence form divA(x,Du)=divG.

Besov regularity for solutions of p-harmonic equations

\text {div }{\mathcal A}(x,Du)=\text {div } G.

Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

When A

Nonlinear Beltrami operators, Schauder estimates and bounds for the Jacobian☆

{\mathcal A}

A note on transport equation in quasiconformally invariant spaces

has linear growth in Du, and assuming that x↦A(x,ξ)

Sharp nonremovability examples for Hölder continuous quasiregular mappings in the plane

x\mapsto {\mathcal A}(x,\xi )

Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities

enjoys Bnα,qα

WEIGHTED ESTIMATES FOR BELTRAMI EQUATIONS

B^{\alpha }_{\frac {n}\alpha , q}

Distortion of Hausdorff measures and improved Painlevé removability for quasiregular mappings

smoothness, local well-posedness is found in Bp,qα