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UID:1cc560507c5b25a08eef53526606d91d
CATEGORIES:Nonlinear Analysis
CREATED:20221205T123938
SUMMARY:Regularity of C^{1,?} Interface Elliptic Transmission Problems
LOCATION:Hill Center Room 705
DESCRIPTION:\n - Abstract: Transmission problems describe phenomena in which a physical
  quantity changes behavior across some fixed surface, known as the interfac
 e. The analysis of such problems started in the 1950s with the pioneering w
 ork of Picone in elasticity. Nowadays, they have a wide range of applicatio
 ns in different areas, such as electromagnetic processes, composite materia
 ls, and climatology. Typically, solutions are not differentiable across the
  interface, and the primary interest is to study their optimal regularity f
 rom each side of this surface. In this talk, I will discuss two elliptic tr
 ansmission problems where the interface has minimal regularity. The first p
 roblem is for harmonic functions, and I will explain the main ideas and tec
 hniques used to prove the optimal regularity of solutions at the boundary. 
 The second problem is for fully nonlinear equations, and I will focus on ho
 w to obtain a maximum principle (ABP estimate) for this problem, which play
 s a key role in the regularity theory of viscosity solutions. These results
  are part of my Ph.D. dissertation, and they are in collaboration with Luis
  Caffarelli and Pablo Raúl Stinga.
X-ALT-DESC;FMTTYPE=text/html:<ul><li><strong>Abstract:&nbsp;</strong>Transmission problems describe phen
 omena in which a physical quantity changes behavior across some fixed surfa
 ce, known as the interface. The analysis of such problems started in the 19
 50s with the pioneering work of Picone in elasticity. Nowadays, they have a
  wide range of applications in different areas, such as electromagnetic pro
 cesses, composite materials, and climatology. Typically, solutions are not 
 differentiable across the interface, and the primary interest is to study t
 heir optimal regularity from each side of this surface. In this talk, I wil
 l discuss two elliptic transmission problems where the interface has minima
 l regularity. The first problem is for harmonic functions, and I will expla
 in the main ideas and techniques used to prove the optimal regularity of so
 lutions at the boundary. The second problem is for fully nonlinear equation
 s, and I will focus on how to obtain a maximum principle (ABP estimate) for
  this problem, which plays a key role in the regularity theory of viscosity
  solutions. These results are part of my Ph.D. dissertation, and they are i
 n collaboration with Luis Caffarelli and Pablo Raúl Stinga.</li></ul>
CONTACT:Maria Soria Carro Rutgers University
DTSTAMP:20260829T003004
DTSTART;TZID=America/New_York:20221206T134000
DTEND;TZID=America/New_York:20221206T144000
SEQUENCE:0
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