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On fractional quasilinear equations with elliptic degeneracy
Damião J. Araújo, Disson dos Prazeres, Erwin Topp
In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local…
Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones
Gabrielle Nornberg, Disson dos Prazeres, Alexander Quaas
In this article we study the fundamental solutions or "-harmonic functions" for some nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such as \begin…
Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy
Pêdra D. S. Andrade, Disson S. dos Prazeres, Makson S. Santos
We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at…
Cordes-Nirenberg type results for nonlocal equations with deforming kernels
Disson dos Prazeres, Aelson Sobral, José Miguel Urbano
We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Ampère eq…
Cavity problems in discontinuous media
Disson dos Prazeres, Eduardo V. Teixeira
We study cavitation type equations, , for bounded, measurable elliptic media . De Giorgi-Nash-Moser theory assures that solut…
Asymptotics and regularity of flat solutions to fully nonlinear elliptic problems
Disson dos Prazeres, Eduardo Teixeira
In this work we establish local regularity estimates for flat solutions to non-convex fully nonlinear elliptic equations provided the coefficients and the source function…