BMO continuity for some heat potentials
BMO estimates near the boundary for solutions of elliptic systems.
Borderline sharp estimates for solutions to Neumann problems.
Bound state solutions for a class of nonlinear Schrödinger equations.
Boundary asymptotic and uniqueness of solution for a problem with -Laplacian.
Boundary behavior and estimates for solutions of equations containing the -Laplacian.
Boundary behaviour in strongly degenerate parabolic equations.
Boundary blow-up solutions for a cooperative system involving the p-Laplacian
We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system in a smooth bounded domain of , where is the p-Laplacian operator defined by with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.
Boundary blow-up solutions of cooperative systems
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