Leonori, TommasoPorretta, Alessio2024-11-202024-11-202015-10-09Leonori, T., & Porretta, A. (2016). Large solutions and gradient bounds for quasilinear elliptic equations. Communications in Partial Differential Equations, 41(6), 952–998. https://doi.org/10.1080/03605302.2016.11692860360-5302; eISSN:1532-4133https://doi.org/10.1080/03605302.2016.1169286https://hdl.handle.net/20.500.14468/24448We consider the quasilinear degenerate elliptic equation λu - Δpu + H(x,Du)= 0 in Ω where Δp is the p-Laplace operator, p > 2, λ ≥0 and Ω is a smooth open bounded subset of ℝN (N ≥ 2). Under suitable structure conditions on the function H, we prove local and global gradient bounds for the solutions. We apply these estimates to study the solvability of the Dirichlet problem, and the existence, uniqueness and asymptotic behavior of maximal solutions blowing up at the boundary. The ergodic limit for those maximal solutions is also studied and the existence and uniqueness of a so-called additive eigenvalue is proved in this context.eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoErgodic problemgradient estimatesP-Laplacianlarge solutionssolvability of the Dirichlet problem