Related papers: Pointwise boundary estimates for fully nonlinear e…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish…
We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form f(Hess, u)=0 on a smoothly bounded domain D in R^n. In our approach the equation is replaced by a subset F of the space of symmetric nxn-matrices,…
Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach…
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…
In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…
Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered:…
We prove a number of \textit{a priori} estimates for weak solutions of elliptic equations or systems with vertically independent coefficients in the upper-half space. These estimates are designed towards applications to boundary value…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
In this survey paper, we study the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains and establish the H\"older continuity of solutions and their derivatives up to the boundary.
We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of…
We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as $$ -F(x,u,Du,D^2u) =\lambda c(x)u+\langle M(x)D u, D u \rangle +h(x) $$ in a bounded domain with a Dirichlet boundary condition, here…
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
As explained in detail in the prologue to this manuscript, boundedness of weak solutions for general classes of elliptic equations in divergence form is a classic tool for achieving higher regularity. We propose here some global boundedness…
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…