| Full text | |
| Author(s): |
Bessa, Junior Da S.
;
da Silva, Joao Vitor
;
Frederico, Maria N. B.
;
Ricarte, Gleydson C.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 264, p. 34-pg., 2026-03-01. |
| Abstract | |
In this manuscript, we establish global weighted Orlicz-Sobolev and variable exponent Morrey-Sobolev estimates for viscosity solutions to fully nonlinear parabolic equations subject to oblique boundary conditions on a portion of the boundary, within the following framework: { F(D(2)u,Du,u,x,t) -ut=f(x,t) in Omega(T), beta & sdot;Du+gamma u=g(x,t)on S-T, u(x,0) = 0 on Omega(0), where Omega T=Omega x (0,T) denotes the parabolic cylinder with spatial base Omega (a bounded domain in R-n, n >= 2, ) and temporal height T>0,S-T=partial derivative Omega x (0,T), and Omega(0)=Omega x {0} . Additionally, f represents the source term of the parabolic equation, while the boundary data are given by beta,gamma, andg . Our first main result is a global weighted Orlicz-Sobolev estimate for the solution, obtained under asymptotic structural conditions on the differential operator and appropriate assumptions on the boundary data, assuming that the source term belongs to the corresponding weighted Orlicz space. Leveraging these estimates, we demonstrate several applications, including a density result within the fundamental class of parabolic equations, regularity results for the related obstacle problem, and weighted Orlicz-BMO estimates for both the Hessian and the time derivative of the solution. Lastly, we derive variable exponent Morrey-Sobolev estimates for the problem via an extrapolation technique, which are of independent mathematical interest. (AU) | |
| FAPESP's process: | 23/18447-3 - Regularity estimates for fully nonlinear ellpitic models with oblique boundary condition and applications |
| Grantee: | Junior da Silva Bessa |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |