Boundary value problem with integral conditions for a linear third-order equation.
Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.
In this paper we consider general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylindersΩ = {(x0,x,t) ∈ R x Rn-1 x R: x0 > A(x,t)}.We prove solvability of Dirichlet, Neumann as well as regularity type problems with data in Lp and Lp1,1/2 (the parabolic Sobolev space having tangential (spatial) gradients and half a time derivative in Lp) for p ∈ (2 − ε, 2 + ε) assuming...
Boundary value problems and layer potentials on manifolds with cylindrical ends
We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...
Boundary value problems as limits of problems in all space
Boundary value problems at resonance for vector second order nonlinear ordinary differential equations
Boundary value problems for elliptic equations.
In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.
Boundary value problems for evolution inclusions
Boundary value problems for evolution inclusions
Boundary value problems for generalized analytic functions of several complex variables
Boundary value problems for linear partial differential equation with constant coefficients. Homogeneous equation in the half plane
Boundary value problems for linear partial differential equation with constant coefficients. Non-homogeneous equation in the halfplane
Boundary value problems for nonlinear partial differential equations in anisotropic Sobolev spaces
Boundary value problems for non-parametric surfaces of prescribed mean curvature
Boundary value problems for partial differential equations with piecewise constant delay.
Boundary value problems for quasielliptic equations in a half-space.
Boundary value problems for quasielliptic systems.
Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle
Boundary value problems for second-order partial differential equations with operator coefficients.
Boundary value problems for some classes of degenerating second order partial differential equations.