Fernando A. Lopez Garcia

Fernando A. Lopez Garcia

Associate Professor, Department of Mathematics and Statistics, College of Science

Email

Phone number

909-869-2496

Office location

Building 8: Room 253

Office hours

M W | 9:30 - 10:30 AM (OFFICE) TH | 10:00 - 12:00 PM (ZOOM)

Research interests

My research interest focuses on certain functional inequalities in Sobolev spaces, such as Poincaré type inequalities, where the geometry of the domain plays a fundamental role. These results are used in the variational analysis of certain partial differential equations and the numerical analysis of their solutions. 
 

Publications 

  1. D. Cruz-Uribe, F. López-García, and I. Ojea, Poincaré and Sobolev inequalities with variable exponents and log-Holder continuity only at the boundary, submitted for publication (2024). pdf

  2. F. López-García, and I. Ojea, Some inequalities on weighted Sobolev spaces, distance weights and the Assouad dimension, submitted for publication (2023). pdf

  3. F. López-García, and I. Ojea, Weighted discrete Hardy inequalities on trees and applications, Potential Analysis 59 (2023), no. 2, 675-703. pdf

  4. G. Bui, F. López-García, and V. Tran, An application of the weighted discrete Hardy inequality, Math. Inequal. Appl., 25 (2022), no. 3, 771-788. pdf

  5. R. Hurri-Syrjänen, and F. López-García, On the weighted fractional Poincaré-type inequalities, Colloq. Math. 157 (2019), no. 2, 213-230. pdf

  6. F. López-García, Weighted generalized Korn inequality on John domains, Math. Methods Appl. Sci. 41 (2018), no. 17, 8003-8018.  pdf

  7. F. López-García, Weighted Korn inequality on John domains, Studia Math. 241 (2018), no. 1, 17-39. pdf

  8. F. López-García, A decomposition technique for integrable functions with applications to the divergence problem, J. Math. Anal. Appl., 418 (2014), no. 1, 79-99. pdf

  9. G. Acosta, R. Durán, and F. López-García, Korn inequality and divergence operator:counterexamples and optimality of weighted estimates, Proc. Amer. Math. Soc. 141 (2013), no. 1, 217-232. pdf

  10. R. Durán, and F. López-García, Solutions of the divergence and Korn inequalities on domains with an external cusp, Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 2, 421-438. pdf

  11. R. Durán, and F. López-García, Solutions of the divergence and analysis of the Stokes equations in planar domains, Math. Models Methods Appl. Sci. 20 (2010), no. 1, 95-120. pdf

Dissertations 

  1. A right inverse of the divergence operator on domains with cusps, Ph.D. Thesis - Universidad de Buenos Aires (2010). pdf (in English)

  2. El Teorema de Khovanskii y un refinamiento a los sistemas trinomiales en el plano, Licentiate Thesis (BS/MS) - Universidad de Buenos Aires (2002). pdf (in Spanish)

Collaborators

Gabriel Acosta (Universidad de Buenos Aires, Argentina)

David Cruz-Uribe (University of Alabama, United States)

Ricardo Durán (Universidad de Buenos Aires, Argentina)

Ritva Hurri-Syrjänen (Univerisity of Helsinki, Finland)

Ignacio Ojea (Universidad de Buenos Aires, Argentina)

Student-Collaborators

Giao Bui (Cal Poly Pomona, United States)

Van Tran (Cal Poly Pomona, United States)