The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition.
The Boubaker polynomials expansion scheme BPES for solving a standard boundary value problem.
The boundary behavior of a composite material
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order in the energy norm.
The boundary behavior of a composite material
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order ε in the energy norm.
The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary value problem for polyanalytic function in multiply-connected region
The boundary value problem of the equations with nonnegative characteristic form.
The boundary-value problem for the transport equation with purely Compton scattering.
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The boundedness of classical operators on variable spaces.
The branch of positive solutions to a semilinear elliptic equation on
The Bremermann-Dirichlet problem for -plurisubharmonic functions
The BV solution of the parabolic equation with degeneracy on the boundary
Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.
The C stability of slow manifolds for a system of singularly perturbed evolution equations
In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C stability of invariant manifolds with respect to small values of the singular parameter.
The Calderón problem with partial data
We describe a joint work with C.E. Kenig and G. Uhlmann [9] where we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension , the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem.
The Calderón Projector for an Elliptic Operator in Divergence Form.
The Calderón-Zygmund theorem and parabolic equations in -spaces
A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in -spaces.
The Calderón-Zygmund theory for elliptic problems with measure data
We consider non-linear elliptic equations having a measure in the right-hand side, of the type and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calderón-Zygmund theory for the problem. All the regularity results presented in this paper are provided together with explicit local a priori estimates.
The C*-Algebra of a Singular Elliptic Problem on a Noncompact Riemannian Manifold.