Related papers: $C^2$ estimate for oblique derivative problem with…
We consider a semilinear elliptic equation with Dirichlet boundary conditions in a smooth, possibly unbounded, domain. Under suitable assumptions, we deduce a condition on the size of the domain that implies the existence of a positive…
In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann…
We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique $W^{1,p}$ solvability is obtained with $p$ being in the optimal range $(4/3,4)$. The leading coefficients are assumed…
We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the…
We prove gradient estimates for solutions of the oblique derivative problem for a large class of elliptic and parabolic quasilinear PDEs. In particular, we expand on previous work of the author using a maximum principle argument. In…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations…
We introduce and study the Dirichlet problem for double divergence form elliptic equations with coefficients of low regularity and boundary conditions given by general Borel measures. Under broad assumptions we establish the solvability of…
In this paper, we study the Dirichlet problem for the implicit degen- erate nonlinear elliptic equation with variable exponent in a bounded domain. We obtain sufficient conditions for the existence of a solution with- out regularization and…
Following the previous work [1], we investigate the impact of damping on the oscillation of smooth solutions to some kind of quasilinear wave equations with Robin and Dirichlet boundary condition. By using generalized Riccati transformation…
We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account is very general and comprises also the singular and…
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with smooth boundary data one can find an approximating equation…
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…
This paper is concerned with H\"older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain,…
We give stability estimates in the Cauchy problem for general partial differential equation of the elliptic type similar to the Helmholtz equation. We do not impose any (pseudo)convexity assumptions on the domain or the operator. These…
We study quasilinear elliptic double obstacle problems with a variable exponent growth when the right-hand side is a measure. A global Calder\'{o}n-Zygmund estimate for the gradient of an approximable solution is obtained in terms of the…
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…
We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of…
Let $L$ be a second order elliptic operator $L$ with smooth coefficients defined on a domain $\Omega $ in $\mathbb{R}^d $, $d\geq3$, such that $L1\leq 0$. We study existence and properties of continuous solutions to the following problem…