7 papers
Large harmonic functions for fully nonlinear fractional operators
Gonzalo Dávila, Alexander Quaas, Erwin Topp
We study existence, uniqueness and boundary blow-up profile for fractional harmonic functions on a bounded smooth domain . We deal with harmonic functions ass…
Periodic homogenization of the principal eigenvalue of second-order elliptic operators
Gonzalo Dávila, Andrei Rodríguez-Paredes, Erwin Topp
In this paper we investigate homogenization results for the principal eigenvalue problem associated to -homogeneous, uniformly elliptic, second-order operators. Under rather gen…
On large solutions for fractional Hamilton-Jacobi equations
Gonzalo Dávila, Alexander Quaas, Erwin Topp
We study the existence of large solutions for nonlocal Dirichlet problems posed on a bounded, smooth domain, associated to fully nonlinear elliptic equations of order , with $s…
Comparison Principles for nonlocal Hamilton-Jacobi equations
Gonzalo Dávila
We prove the comparison principle for viscosity sub and super solutions of degenerate nonlocal operators with general nonlocal gradient nonlinearities. The proofs apply to purely H…
The Nonlocal Inverse Problem of Donsker and Varadhan
Gonzalo Dávila, Erwin Topp
In this paper we prove a nonlocal version of the celebrated Inverse Problem of Donsker and Varadhan~\cite{DV} for nonlocal elliptic operators of the form $$ \cL u = L_K u + \cB_K (…
Regularity for parabolic systems with critical growth in the gradient and applications
Agnid Banerjee, Gonzalo Dávila, Yannick Sire
Motivated by problems arising in geometric flows, we prove several regularity results for systems of local and nonlocal equations, adapting to the parabolic case a neat argument du…