Anthony Matos

Anthony Matos

Mentor

Lei Zhang, PhD

College

College of Liberal Arts and Sciences

Major

Mathematics

Minor

N/A

Organizations

University Math Society

Academic Awards

Phi Beta Kappa, Deans list.

Volunteering

N/A

Research Interests

Analysis of PDEs, geometric analysis

Hobbies and Interests

Music

Research Project

On the Best Constant on Sobolev’s Inequality

In mathematical analysis, a Sobolev inequality is an inequality which controls the magnitude of lower order derivatives of a function by the magnitude of higher order derivatives. The simplest Sobolev inequality is the one originally discovered by Sobolev in his seminal 1938 paper On a theorem in functional analysis, which controls an integral norm of a function by an integral norm of its gradient. The aim of this project is to find an alternative proof to ones existing in the literature finding the best possible constant in Sobolev’s inequality.

  • Lei Zhang, PhD
  • Mathematics
  • N/A
  • Analysis of PDEs, geometric analysis
  • Phi Beta Kappa, Deans list.
  • University Math Society
  • N/A
  • Music
  • On the Best Constant on Sobolev’s Inequality
  • In mathematical analysis, a Sobolev inequality is an inequality which controls the magnitude of lower order derivatives of a function by the magnitude of higher order derivatives. The simplest Sobolev inequality is the one originally discovered by Sobolev in his seminal 1938 paper On a theorem in functional analysis, which controls an integral norm of a function by an integral norm of its gradient. The aim of this project is to find an alternative proof to ones existing in the literature finding the best possible constant in Sobolev’s inequality.