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 regularity of weak solutions to nonlinear elliptic obstacle problems.
Boundary Regulartiy for certain quasilinear elliptic systems of divergence structure.
Boundary sentinels in cylindrical domains.
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
Boundary sentinels with given sensitivity.
Boundary singularities of solutions of sublinear elliptic equations.
Boundary singularities of solutions to quasilinear elliptic equations
Asymptotic formulae for solutions to boundary value problems for linear and quasilinear elliptic equations and systems near a boundary point are discussed. The boundary is not necessarily smooth. The main ingredient of the proof is a spectral splitting and reduction of the original problem to a finite-dimensional dynamical system. The linear version of the corresponding abstract asymptotic theory is presented in our new book “Differential equations with operator coefficients”, Springer, 1999.
Boundary stabilization of a coupled system of nondissipative Schrödinger equations.
Boundary stabilization of a hyperbolic equation with viscosity.
Boundary stabilization of Maxwell’s equations with space-time variable coefficients
We consider the stabilization of Maxwell’s equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard” identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks.
Boundary stabilization of Maxwell's equations with space-time variable coefficients
We consider the stabilization of Maxwell's equations with space-time variable coefficients in a bounded region with a smooth boundary by means of linear or nonlinear Silver–Müller boundary condition. This is based on some stability estimates that are obtained using the “standard" identity with multiplier and appropriate properties of the feedback. We deduce an explicit decay rate of the energy, for instance exponential, polynomial or logarithmic decays are available for appropriate feedbacks. ...
Boundary stabilization of the Schrödinger equation in almost star-shaped domain
Boundary Subspaces for the Finite Element Method With Lagrange Multipliers.
Boundary trace of positive solutions of nonlinear elliptic inequalities
We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of in a smooth domain under very general assumptions on . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the nonlinearity...
Boundary trace of solutions of semilinear elliptic equalities and inequalities
The boundary trace problem for positive solutions of is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.
Boundary value problem for Fuchsian partial differential equations and reflection of singularities
Boundary Value Problem for Nonlinear Singularity perturbed Systems in Critical case of Exchange of Stability
Boundary value problem for second-order differential operators with mixed nonlocal boundary conditions.