We investigate the existence, asymptotic boundary behavior and uniqueness of boundary blow-up viscosity solutions in a bounded domain Ω of partial Laplace equations with a nonlinear zero-order term f(u) of Keller-Osserman type and a non homogeneous term h(x). The main difficulty in the investigation rests on the possibility that the equation is very degenerate elliptic, and h is unbounded as well as sign-changing in Ω. To the best of our knowledge, large solutions to equations involving partial trace operators have not been investigated before.
Blow-up solutions for partial Laplace equations with Keller–Osserman condition
A. Vitolo
2026
Abstract
We investigate the existence, asymptotic boundary behavior and uniqueness of boundary blow-up viscosity solutions in a bounded domain Ω of partial Laplace equations with a nonlinear zero-order term f(u) of Keller-Osserman type and a non homogeneous term h(x). The main difficulty in the investigation rests on the possibility that the equation is very degenerate elliptic, and h is unbounded as well as sign-changing in Ω. To the best of our knowledge, large solutions to equations involving partial trace operators have not been investigated before.File in questo prodotto:
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