Related papers: Oblique Derivative Problems for Elliptic Equations…
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those equations regards the existence of a lower bound to the…
In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\alpha$-H\"older continuous…
In this paper, we prove a boundary pointwise regularity for fully nonlinear elliptic equations on cones. In addition, based on this regularity, we give simple proofs of the Liouville theorems on cones.
We provide a sharp $C^{1,\alpha}$ estimate up to the boundary for a viscosity solution of a degenerate fully nonlinear elliptic equation with the oblique boundary condition on a $C^1$ domain. To this end, we first obtain a uniform boundary…
We prove the existence and $C^{1,\alpha}$ regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be $C^1$ or…
We study regularity of solutions $u$ to $\overline\partial u=f$ on a relatively compact $C^2$ domain $D$ in a complex manifold of dimension $n$, where $f$ is a $(0,q)$ form. Assume that there are either $(q+1)$ negative or $(n-q)$ positive…
We consider stable solutions of a semilinear elliptic equation with homogeneous Neumann boundary conditions. A classical result of Casten, Holland [20] and Matano [44] states that all stable solutions are constant in convex bounded domains.…
In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varying characteristic exponents.
In this paper, we investigate the boundary H\"{o}lder regularity for elliptic equations (precisely, the Poisson equation, linear equations in divergence form and non-divergence form, the p-Laplace equations and fully nonlinear elliptic…
In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the higher regularity of the free boundaries in obstacle-type…
In this paper, we investigate the oblique boundary value problem for degenerate Hessian quotient type equations in a smooth bounded domain. Without imposing any geometric restrictions on the domain, we establish the a priori estimates and…
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses and on the regularity of the solutions to the associated…
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
We study the Possion problem with singular data given by a source supported on a one dimensional curve strictly contained in a three dimensional domain. We prove regularity results for the solution on isotropic and on anisotropic weighted…
In two dimensions every weak solution to a nonlinear elliptic system $\rm{div} a(x,u,Du)=0$ has H\"older continuous first derivatives provided that standard continuity, ellipticity and growth assumptions hold with a growth exponent $p \geq…
In this paper, we continue our investigations into the global theory of oblique boundary value problems for augmented Hessian equations. We construct a global barrier function in terms of an admissible function in a uniform way when the…
In bounded domains, without any geometric conditions, we study the existence and uniqueness of globally Lipschitz and interior strong C^{1,1}, (and classical C^2), solutions of general semilinear oblique boundary value problems for…
We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey…
We prove the optimal $W^{2, \infty }$ regularity for fully nonlinear elliptic equations with convex gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be $C^1$ or strictly convex. We…