We establish new global regularity estimates for the Hessian of viscosity solutions to non-convex fully nonlinear elliptic equations with oblique boundary conditions in the setting of weighted Lorentz and Morrey-Lorentz spaces. More precisely, our approach relies on an analysis of the ellipticity coefficients of the governing operator and, under suitable small-aperture assumptions, we obtain Calderón-Zygmund type estimates in weighted Lorentz spaces. As a byproduct of this result, we derive several applications, including Sobolev estimates with variable exponents and the study of the obstacle problem with an oblique boundary condition.
In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combin...
J. V. da Silva, Junior da Silva Bessa, Laura Ospina· Annales Fennici Mathematici· 0 citations
We establish the regularity properties of adjoint solutions to elliptic equations in double divergence form with variable coefficients and rough forcing terms. More precisely, we consider Dirichlet problems associated with the formal adjoint of second-order elliptic operators in non-divergence form, assuming that the...
G. Di Fazio, Dennys Sberna· Zeitschrift für Analysis und...· 1 citation
In this paper, we establish boundary C1,α regularity for viscosity solutions to a class of singular and degenerate fully nonlinear elliptic equations subject to oblique boundary conditions. Our work extends the findings in Byun et al (2025 Calc. Var. PDE 64 20) to a broader class of equations, notably encompassing the...
Sun-Sig Byun, Hongsoo Kim, Seunghyun Kim· Nonlinearity· 0 citations
The known proofs of the gradient estimate for complex Hessian equations rely on the second order estimate of Hou-Ma-Wu and on a Liouville theorem of Dinew-Kolodziej. In this paper, we give a direct proof of the gradient estimate for concave fully nonlinear elliptic equations on compact Hermitian manifolds, which uses n...
It is known that a major difficulty in proving H\"{o}lder regularity for solutions to quasilinear singular parabolic equations of $p$-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular paraboli...
This paper investigates the well-posedness and hidden regularity of boundary-degenerate hyperbolic equations in a two-dimensional setting. The shape design method is employed, which approximates the original degenerate problem by a family of uniformly elliptic problems on truncated subdomains and passes to the limit th...
Donghui Yang, Hong-Lin Sun· 0 citations
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