Boundary blow-up solutions to -Laplacian equations with exponential nonlinearities.
Boundary estimates for certain degenerate and singular parabolic equations
We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular...
Boundary estimates for solutions of Monge-Ampère equations in the plane
Boundary estimates for solutions of nonlinear degenerate parabolic systems.
Boundary feedback stabilization of a hybrid PDE-ODE system.
Boundary homogenization for a quasi-linear elliptic problem with Dirichlet boundary conditions posed on small inclusions distributed on the boundary.
Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate to the quasi-neutral...
Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate to the quasi-neutral...
Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to...
Boundary layer for Chaffee-Infante type equation
This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly" constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary.
Boundary layer tails in periodic homogenization
Boundary layer tails in periodic homogenization
This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period ε): first, they add...
Boundary layers for transmission problems with singularities.
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case.
Boundary problems of the second order with an indefinite weight-function.
Boundary regularity for certain fully nonlinear elliptic equations.
Boundary regularity for solutions of the equation of prescribed Gauss curvature
Boundary regularity of flows under perfect slip boundary conditions
We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.
Boundary regularity of solutions of the inhomogeneous Cauchy-Riemann equations
Boundary Regulartiy for certain quasilinear elliptic systems of divergence structure.