Analysis and Partial Differential Equations

Analysis and Partial Differential Equations

The research in Analysis and Partial Differential Equations at the BGSMath covers a broad range of topics, from classical function theory in one and several complex variables to the study of Banach spaces and its operators. The interplay between singular operators and geometric function theory has been very succesful.

On PDE’s the research at the BGSMath is centered around reaction-diffusion and integro-differential equations (regularity and qualitative properties of solutions), population dynamics and biological evolution, as well as several wave problems in mathematical physics and mathematical modelling.

Research Lines

Complex Analysis and Potential Theory

Keywords: Spaces of holomorphic functions. Operator theory.  Interpolation and sampling. Point processes. Capacities and energy.

Joaquim Bruna (UAB)
Carme Cascante (UB)
Albert Clop (UAB)
Konstantin Dyakonov (UB)
Jordi Marzo (UB)
Xavier Massaneda (UB)
Artur Nicolau (UB)
Joaquim Ortega Cerdà (UB)
Jordi Pau (UB)

Nonlinear elliptic and parabolic Partial Differential Equations

Keywords: Reaction-diffusion problems. Nonlocal fractional diffusion equations. Isoperimetric and Sobolev inequalities. Structured population dynamics. Qualitative theory of partial differential equations

Xavier Cabré (UPC)
Angel Calsina (UAB)
Silvia Cuadrado (UAB)
Joan Solà-Morales (UPC)

Harmonic Analysis and Geometric Measure Theory

Keywords: Singular operators. Calderon-Zygmund theory.  Quasiconformal maps. Analytic capacity. Rectifiability. Euler and aggregation equations. p-harmonic functions

Albert Clop (UAB)
Joan Mateu (UAB)
Artur Nicolau (UAB)
Xavier Tolsa (UAB)
Joan Verdera (UAB)

Real and Functional Analysis

Keywords: Maximal operators and the Hilbert transform. Interpolation and extrapolation theory. Rearrangement estimates. Function spaces. Discrete harmonic analysis. Fourier multipliers.

Santiago Boza (UPC)
María Jesús Carro (UB)
Joaquim Martín (UAB)
Javier Soria (UB)
Sergey Tikhonov (CRM)

Links to research groups

Researchers in the Barcelona area, and more generally in Catalonia, group themselves into smaller research groups, following not only academic but also administrative criteria, like location or research grants.