This paper studies the exterior Dirichlet problem for Hessian quotient equations with nonconstant right-hand sides. We prove the existence of classical admissible solutions with prescribed asymptotic Hessians and establish convergence of the Hessian at infinity. The main difficulties are obtaining second-order estimates on expanding annuli that are uniform in the outer radius and deriving Hessian convergence under an integral tail condition with no prescribed decay rate. These are resolved through a radius-independent boundary-to-interior estimate and a blow-down argument. We also allow nonradial perturbations of the source. Under stronger pointwise assumptions, we obtain higher-order asymptotic expansions and solutions for every sufficiently large prescribed asymptotic constant.
We establish the existence and uniqueness theorem for the exterior Dirichlet problem for the special Lagrangian equation with prescribed asymptotic behavior at infinity, in both the viscosity setting for all the phases and classical setting for the critical and supercritical phases. These results generalize previous wo...
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
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 go...
Junior da Silva Bessa· Analysis and Applications· 0 citations
This paper presents a mathematical analysis of the inverse problem concerning the recovery of two unknown potential coefficients in a coupled Schrödinger equations system, within a bounded domain of the Euclidean space Rn with Dirichlet boundary conditions. Our analysis relies on Neumann boundary measurements, where we...
In this paper, we study the global regularity of oblique boundary value problems for n-1 type augmented Hessian equations on a bounded domain, without imposing any convexity condition either on the domain or on the matrix-valued function in the n-1 type augmented Hessian equations. We establish a global existence and u...
This paper investigates entire classical separable variable radial solutions to a class of parabolic k-Hessian equations -u_t (sigma_k(lambda(D^2u)))^alpha = f(|x|)g(t), where the right-hand side consists of positive continuous functions. Without assuming that -u_t is positively bounded, we extend previous work for the...
Ning An, Ji-Guang Bao· 0 citations
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