arXiv subjects
Publications and source records attributed to Nikolai Ubostad.
We study the boundary regularity for the normalised $\infty$-heat equation $u_t = Δ_{\infty}^Nu$ in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions, and prove an Exterior Ball result. A Petrovsky-like criterion is established.
The boundary regularity for the normalized $p$-parabolic equation $u_t =\frac{1}{p}|Du|^{2-p}Δ_pu$ is studied. Perron's method is used to construct solutions in arbitrary domains. We classify the regular boundary points in terms of barrier functions, and prove an Exterior Sphere result. A fundamental solution is identified. A Petrovsky criterion is established, and we examine the convergence of solutions as $p \to \infty$.
We investigate a degenerate elliptic PDE related to the $\infty$-Laplace equation $Δ_{\infty}u=0$. A stability result is derived. The $Γ$-convergence of the corresponding functionals is investigated.