Harmonic Mappings and Minimal Submanifolds.
Harmonic maps which solve a free-boundary problem.
Heat flow and boundary value problem for harmonic maps
Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree we prove the optimal rates of convergence in the -norm and in the -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account....
Higher order nonlinear partial differential equations in unbounded domains of
Higher regularity for nonlinear oblique derivative problems in Lipschitz domains
There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients as well...
Higher regularity of weak solutions of strongly nonlinear elliptic equations
Hölder regularity for nonhomogeneous elliptic systems with nonlinearity greater than two
Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension is less than or equal to .
Holes and obstacles
Homogénéisation des équations de la diffusion stationnaire dans les domaines cylindriques aplatis
Homogenization of elliptic problems in a fiber reinforced structure. Non local effects
Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary
H-surface index formula
Hypersurfaces of constant curvature in hyperbolic space II
This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.