Global weighted Lorentz estimates of oblique tangential derivative problems for weakly convex fully nonlinear operators
Abstract
In this work, we develop weighted LorentzSobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration $F(D^{2}u, Du, u, x) = f(x)$ in $\Omega$ and $\beta\cdot Du+\gamma u=g$ on $\partial \Omega$, where $\Omega$ is a bounded domain in $\mathbb{R}^{n}$ ($n \geq 2$), under suitable assumptions on the source term f, data $\beta$, $\gamma$ and g. In addition, we obtain LorentzSobolev estimates for solutions to the obstacle problem and others applications.
 Publication:

arXiv eprints
 Pub Date:
 February 2023
 DOI:
 10.48550/arXiv.2302.09177
 arXiv:
 arXiv:2302.09177
 Bibcode:
 2023arXiv230209177B
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 25 pages