S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
Regularity theory for elliptic and parabolic equations in nondivergence form
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- Regularity; nondivergence elliptic equation; nondivergence parabolic equation; strong solution; BMO space; weighted Lebesgue space; Orlicz space; variable exponent Lebesgue space
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 변순식.
- We investigate optimal regularity theory for nondivergence elliptic and parabolic equations with discontinuous coefficients in bounded domains.
Global Hessian estimates of the solutions to the Dirichlet problems for such equations are obtained under the small bounded mean oscillation (BMO) condition of the coefficients in the setting of various function spaces such as weighted Lebesgue spaces, variable exponent Lebesgue spaces, weighted Orlicz spaces and weighted variable exponent Lebesgue spaces.