Metric tensor estimates, geometric convergence, and inverse boundary problems.
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.
We construct geometric barriers for minimal graphs in We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In , we solve the Dirichlet problem for the vertical minimal equation in a convex domain taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...
A multiplicative structure in the cohomological version of Conley index is described following a joint paper by the author with K. Gęba and W. Uss. In the case of equivariant flows we apply a normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is applied then to obtain a mountain pass type theorem. Another illustrative application is a result on multiple bifurcations for some elliptic PDE.
We prove the existence of solutions to , together with appropriate boundary conditions, whenever is a maximal monotone graph in , for every fixed . We propose an adequate setting for this problem, in particular as far as measurability is concerned. It consists in looking at the graph after a rotation, for every fixed ; in other words, the graph is defined through , where is a Carathéodory contraction in . This definition is shown to be equivalent to the fact that is pointwise monotone...