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Applied Analysis
Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～
| Date, time & place | Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.) |
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2025/04/17
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
Shuhei KITANO (The University of Tokyo)
On Calderón–Zygmund Estimates for Fully Nonlinear Equations (Japanese)
[ Abstract ]
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
The Calderón–Zygmund estimate provides a bound on the $L^p$ norms of second-order derivatives of solutions to elliptic equations. Caffarelli extended this result to fully nonlinear equations, requiring the exponent $p$ to be sufficiently large. In this work, we explore two generalizations of Caffarelli’s result: one concerning small values of $p$ and the other involving equations with $L^n$ drift terms.
