Boundary asymptotic and uniqueness of solution for a problem with -Laplacian.
Boundary behavior and estimates for solutions of equations containing the -Laplacian.
Boundary behavior of blow-up solutions to some weighted nonlinear differential equations.
Boundary blow-up solutions of cooperative systems
Boundary blow-up solutions to -Laplacian equations with exponential nonlinearities.
Boundary eigencurve problems involving the -Laplacian operator.
Boundary higher integrability for the gradient of distributional solutions of nonlinear systems
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case.
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 weak solutions to nonlinear elliptic obstacle problems.
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 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 problems for non-parametric surfaces of prescribed mean curvature
Bounded nonlinear perturbations of second order linear elliptic problems
Bounded weak solutions to nonlinear elliptic equations.
Boundedness and integrability properties of weak solutions of quasilinear elliptic systems.