Year: 2026
Type: preprint
Abstract: For $p>1$, we consider the boundary value problem for fully nonlinear degenerate elliptic equations $-λ_i(D^2u)+|Du|^p+γu=f(x)$ in bounded domains with Dirichlet or boundary blow-up conditions; here $λ_i(D^2u)$ denotes the $i$-th eigenvalue of the Hessian. We study existence and nonexistence of solutions together with the asymptotic behaviour of the solutions when $γ$ goes to zero. A priori Lipschitz estimates play an important role. The interplay between the operator's degeneracy and the superlinear growth of the Hamiltonian gives rise to phenomena that are very different depending on which of the two terms dominates, e.g. the ergodic dichotomy takes place only when $i=N$, while new phenomena arise for $i
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172382771