1. Quasiconformal Mappings and the Calculus of Variations

1.1 Compensated Compactness and Lower Semicontinuity

Daniel Faraco, André Guerra: A short proof of Ornstein's non-inequality in \(\mathbb{R}^{2×2}\), The Quarterly Journal of Mathematics 73 (2022), no. 1, 17–21, Doi

Pablo Angulo, Daniel Faraco, Carlos García-Gutiérrez: The 2+1 convex hull of a finite set arXiv (2018)

Marcos Oliva: Bi-Sobolev homeomorphisms \(f\) with \(Df\) and \(Df^{-1}\) of low rank using laminates arXiv, Calc. Var.

Daniel Faraco, Carlos Mora-Corral and Marcos Oliva: Sobolev homeomorphisms with gradients of low rank via laminates Preprint, Adv. Calc. Var.

Duvan Henao, Carlos Mora-Corral and Marcos Oliva: Global invertibility of Sobolev maps arXiv

André Guerra, Lukas Koch, Sauli Lindberg: Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs arXiv (2020)

André Guerra, Lukas Koch, Sauli Lindberg: Energy Minimisers with Prescribed Jacobian, Arch Rational Mech Anal 242, 1059–1090 (2021), Doi

André Guerra, Lukas Koch, Sauli Lindberg: The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces, Calc. Var. Partial Differential Equations 60 (2021), no. 1, Paper No. 55, 14 pp., Doi

Sauli Lindberg: On the Hardy space theory of compensated compactness quantities arXiv, Arch. Rational Mech. Anal.

José C. Bellido and Carlos Mora-Corral: Lower semicontinuity and relaxation via Young measures for nonlocal variational problems and applications to peridynamics Preprint

Carlos Mora-Corral and Magdalena Strugaru: Necking in 2D incompressible polyconvex materials: theoretical framework and numerical simulations Preprint

Duvan Henao, Carlos Mora-Corral and Xianmin Xu: A numerical study of void coalescence and fracture in nonlinear elasticity Preprint, Comput. Methods Appl. Mech. Engrg.

Stanislav Hencl and Carlos Mora-Corral: Diffeomorphic approximation of continuous almost everywhere injective Sobolev deformations in the plane Preprint, Quart. J. Math.

José C. Bellido, Carlos Mora-Corral and Pablo Pedregal: Hyperelasticity as a \( \Gamma \)-limit of Peridynamics when the horizon goes to zero Preprint, Calc. Var.

Marco Barchiesi, Duvan Henao and Carlos Mora-Corral: Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity Preprint, Arch. Rational Mech. Anal.

1.2 Beltrami Equations

Kari Astala, Albert Clop, Daniel Faraco, Jarmo Jääskeläinen, Aleksis Koski: Improved Hölder regularity for strongly elliptic PDEs, J. Math. Pures Appl. (9) 140 (2020), 230–258, Doi

Kari Astala, Albert Clop, Diego Faraco, Jarmo Jääskeläinen and Aleksis Koski: Nonlinear Beltrami Operators, Schauder Estimates And Bounds For The Jacobian Preprint, Ann. I. H. Poincare (C)

Kari Astala, Albert Clop, Daniel Faraco and Jarmo Jääskeläinen: Manifolds of quasiconformal mappings and the nonlinear Beltrami equation arXiv

Martí Prats: Beltrami equations in the plane and Sobolev regularity arXiv(to appear in Commun. Pur. Appl. Anal.)

Marcos Oliva and Martí Prats: Sharp bounds for composition with quasiconformal mappings in Sobolev spaces arXiv, JMAA

1.2 Miscellanea

Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi: A Nonlinear Mean Value Property for Monge-Ampère arXiv

Alberto Dayan: Zeros of Normalized Sections of Non Convergent Power Series arXiv

Pablo Angulo: Linking curves, sutured manifolds and the Ambrose conjecture for generic 3-manifolds arXiv, DCDS

2. Inverse Problems

2.1 Limiting Carleman Weights and Conformal Geometry

Pablo Angulo-Ardoy, Daniel Faraco, Luis Guijarro, Mikko Salo: Limiting Carleman weights and conformally transversally anisotropic manifolds, Trans. Amer. Math. Soc. 373 (2020), no. 7, 5171–5197, Doi

Pablo Angulo, Daniel Faraco and Luis Guijarro: Sufficient conditions for the existence of limiting Carleman weights arXiv, Forum of mathematics - Sigma, Sage (section 5), Sage (section 6), Sage (section 7)

Pablo Angulo: On the set of metrics without local limiting Carleman weights arXiv, Inverse Problems and Imaging

Pablo Angulo, Daniel Faraco, Luis Guijarro and Alberto Ruiz: Obstructions to the existence of limiting Carleman weights arXiv, APDE

2.2 The Buckgheim method and the non elliptic Schrödinger equation

Jorge Tejero: Reconstruction of rough potentials in the plane arXiv

Evgeny Lakshtanov, Jorge Tejero and Boris Vainberg: Uniqueness in the inverse conductivity problem for complex-valued Lipschitz conductivities in the plane arXiv

Jorge Tejero: Reconstruction and stability for piecewise smooth potentials in the plane arXiv (to appear in SIMA)

Kari Astala, Daniel Faraco and Keith M. Rogers: Unbounded Potential Recovery in the Plane Preprint (to appear in Annales scientifiques de l’École Normale Supérieure)

Kari Astala, Daniel Faraco and Keith M. Rogers: On Plancherel's identity for a two-dimensional scattering transform Preprint, Nonlinearity

Kari Astala, Daniel Faraco and Keith M. Rogers: Recovery of the Dirichlet-to-Neumann map from scattering data in the plane Preprint (to appear in Kokyuroku Bessatsu)

2.3. Stability, reconstruction and recovery of singularities

Daniel Faraco and Martí Prats: Characterization for stability in planar conductivities arXiv (to appear in J. Differential Equations)

Daniel Faraco, Yaroslav Kurylev and Alberto Ruiz: G-Convergence, Dirichlet to Neumann maps and invisibility arXiv, J. Funct. Anal.

J.A. Barceló, Daniel Faraco, Alberto Ruiz and Ana Vargas: Reconstruction of Discontinuities from Backscattering Data in Two Dimensions preprint, SIAM J. Math. Anal.

Gen Nakamura and Marcos Oliva: Exponential decay of solutions to initial boundary value problem for anisotropic visco-elastic systems Rend. Istit. Mat. Univ. Trieste

3. Fluid mechanics

3.1 MHD

Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr: arXiv

Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr: Rigorous results on conserved and dissipated quantities in ideal MHD turbulence, Geophysical and Astrophysical Fluid Dynamics, published online (2022), Doi

Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr: Bounded solutions of ideal MHD with compact support in space-time arXiv

Daniel Faraco, Sauli Lindberg, David MacTaggart, Alberto Valli: On the proof of Taylor's conjecture in multiply connected domains, Appl. Math. Lett. 124 (2022), Paper No. 107654, 7 pp., Doi

Daniel Faraco, Sauli Lindberg: Proof of Taylor's conjecture on magnetic helicity conservation, Comm. Math. Phys. 373 (2020), no. 2, 707–738, Doi

Diego Alonso-Orán: Asymptotic shallow models arising in magnetohydrodynamics arXiv

Daniel Faraco and Sauli Lindberg: Magnetic helicity and subsolutions in ideal MHD arXiv

3.2 IPM and Instabilities

Ángel Castro, Daniel Faraco, Francisco Mengual: Localized mixing zone for Muskat bubbles and turned interfaces, Ann. PDE 8 (2022), Paper No. 7, 50 pp., Doi

Víctor Arnaiz, Ángel Castro, Daniel Faraco: Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime, Comm. Partial Differential Equations 46 (2021), no. 1, 135–164, Doi

Ángel Castro, Diego Córdoba, Daniel Faraco: Mixing solutions for the Muskat problem, Invent. Math. 226 (2021), no. 1, 251–348, Doi

Lauri Hitruhin, Sauli Lindberg: Lamination convex hull of stationary incompressible porous media equations, SIAM J. Math. Anal. 53 (2021), no. 1, 491–508, Doi

F. Mengual: H-principle for the 2D incompressible porous media equation with viscosity jump Anal. PDE

O. Sanchez: Steady-state solutions for the Muskat problem Collectanea Mathematica

F. Mengual; L. Székelyhidi Jr.: Dissipative Euler flows for vortex sheet initial data without distinguished sign Comm. Pure Appl. Math.