Surfaces of minimum capacity for a knot
A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on
A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C.
This is the first in a series of papers where we intend to show, in several steps, the existence of classical (or as classical as possible) solutions to a general two-phase free-boundary system. We plan to do so by: (a) constructing rather weak generalized solutions of the free-boundary problems, (b) showing that the free boundary of such solutions have nice measure theoretical properties (i.e., finite (n-1)-dimensional Hausdorff measure and the associated differentiability...
On Abel summability of multiple Jacobi series
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
The obstacle problem for the biharmonic operator
Monotonicity of the free boundary in the two-dimensional dam problem
Optimal regularity for one-dimensional porous medium flow.
We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.
Regularity of the boundary of a capillary drop on an inhomogeneous plane and related variational problems.
Abrupt and smooth separation of free boundaries in flow problems
A free boundary problem for quasi-linear elliptic equations
The Dirichlet problem for the degenerate Monge-Ampère equation.
Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (uij) = 0 in Ω u = φ given on ∂Ω.
Regularity of a free boundary with application to the Pompeiu problem.
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