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Fernando A. Lopez Garcia

Fernando A. Lopez Garcia

Associate Professor

Department of Mathematics and Statistics, College of Science

Email

fal@cpp.edu

Phone number

909-869-2496

Office location

Building 8 - Room 253

Office hours

M F | FROM NOON TO 1:00 PM IN OFFICE 8-253 T | FROM 10:00 TO NOON VIA 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. G. Acosta, R. Durán, I. Drelichman, F. López-García, and I. Ojea, The fractional Korn inequality on uniform domains and new Korn inequalities for truncated seminorms, submitted for publication (2026). pdf

  2. F. López-García, and J. Rodriguez, Weighted graphs in the sense of John and a global Poincaré inequality, submitted for publication (2025). pdf

  3. D. Cruz-Uribe, F. López-García, and I. Ojea, Poincaré and Sobolev inequalities with variable exponents and log-Holder continuity only at the boundary, accepted for publication in Potential Analysis (2025). pdf

  4. F. López-García, and I. Ojea, Some inequalities on weighted Sobolev spaces, distance weights and the Assouad dimension, Mathematische Nachrichten 298 (2025), no. 8, 2749-2769. pdf

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

  6. 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

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

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

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

  10. 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

  11. 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

  12. 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

  13. 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/IMAS & Conicet, Argentina)

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

Irene Drelichman (Universidad Nacional de La Plata & Conicet, Argentina)

Ricardo Durán (Universidad de Buenos Aires/IMAS & Conicet, Argentina)

Ritva Hurri-Syrjänen (Univerisity of Helsinki, Finland)

Ignacio Ojea (Universidad de Buenos Aires/IMAS & Conicet, Argentina)

Student-Collaborators

Giao Bui (Cal Poly Pomona, United States)

Van Tran (Cal Poly Pomona, United States)

John Rodriguez (University of Washington)