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 uniqueness theory for classical elliptic solutions by deriving global a priori estimates up to second-order derivatives. Besides the known applications for n-1 type Monge-Ampere operators in optimal transportation and geometric optics, the general theory here embraces equations raised by Li-Sheng, Some Dirichlet problems arising from conformal geometry. Pac. J. Math. 251, 2011, 337-359 and Guan-Qiu-Yuan, Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms. Adv. Math. 343, 2019, 538-566.
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
We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving the $p$-moments of measure-valued traces. We also derive the optimality conditions, which turn out to be matrix-valued generalizations of pres...
Aleksei Kroshnin, Hugo Lavenant, D. Vorotnikov· 0 citations
We study the initial–boundary value problem for a fractional nonlinear Klein–Gordon equation posed on the hyperoctant Dn,n⩾2 with nonhomogeneous boundary data on each coordinate hyperplane. The equation involves a spatial fractional Laplacian of Caputo type with order β∈(3/2,2), which induces strong nonlocal dissipatio...
We study a fractional logistic-type elliptic problem on a bounded domain with homogeneous exterior conditions and linear and nonlinear integral interactions. The interaction kernels may be nonsymmetric and sign-changing, so the problem need not admit a variational formulation. In the symmetric competitive regime, coerc...
Alireza Khatib, S. Mousavinasr, Bashir Zeimarani· 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...
