Harmonic Analysis and PDEs
Objective:This scientific proposal covers a broad scope of problems within the harmonic analysis in Euclidean and non-Euclidean settings, pursuing applications to partial differential equations (PDEs). Here it is an account of the topics that will be treated. -Estimates concerning directional Rubio de Francia square functions. -Regularity of the HardyLittlewood maximal function in various smooth spaces. -Fourier restriction theory, sharp constants in the inequalities as well as what are the extremizing functions. -Fourier interpolation formulas and uncertainty principles in Fourier analysis, connections to number theory and discrete geometry. -Discrete harmonic analysis and connection with ergodic theory. - Non-commutative theory in nilpotent groups. -Harmonic analysis and nonlocal operators in the Heisenberg group. -Fractional discrete Laplacian and unique continuation -Degenerate Elliptic PDE and sharp degenerate Fractional Poincaré and Poincaré-Sobolev inequalities. -Poincaré-Sobolev inequalities in the multiparameter setting. -Theory of weights: the $C_p$ class in connection with various central operators like square functions; optimal bounds for reverse H\"older inequalities; operators on Lorentz spaces.-Multiparameter harmonic analysis, optimal weighted bounds. -Harmonic analysis in the infinite-dimensional torus. -Multilinear operators in harmonic analysis: weighted norm inequalities of operators and vector-valued extensions in the context of general Banach spaces.
MATH4SPORTS - Modelización matemática para la industria deportiva: salud y rendimiento
MATH4SPORTS seeks to transfer applied mathematics as a driving technology to the field of the sports industry, with a high potential for technology transfer to start-ups, professional clubs, researchers and other agents in the innovative environment of Bizkaia.
M-KONTAK - Investigación de los Fenómenos Asociados al Contacto Metal-Metal en Tecnologías de H2 a Alta Presión
The main objective of the M-KONTAK project is to gain an in-depth understanding of the failure modes and their effect on metallic materials and the surfaces of threaded joints in candidate technologies for high-pressure H2 effect on the metallic materials and surfaces that make up the threaded jo
KAIROS - Digitalización predictiva del comportamiento a largo plazo de materiales poliméricos composites. Empleo de IA, modelización basada en la física y metodologías de aceleración de ensayos
KAIROS was created with the main objective of researching and obtaining a solution that allows multi-scale digitisation combined with ML and accelerated testing methodologies, for the study of the long-term behaviour (creep, fatigue, ageing) of polymeric materials applicable, for example, to the
CHARGER+ - Nueva Generación de Puntos de Recarga de Vehículo Eléctrico con Funcionalidades Autónomas y Colaborativas e Impacto Cero
The general objective of the CHARGER+ project is to generate the necessary knowledge to define a new generation of electric vehicle (EV) charging points, so that the related Basque companies (electricity companies, charging post installation companies and charger manufacturers) will be in an adva