Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack.
Singularities of Maxwell’s system in non-hilbertian Sobolev spaces
We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space and an explicit singular one.
Regularity of Transmission Problems in Dihedral Domains
We consider the transmission problem for the Laplace operator in a straight cylinder with data in . Applying the theory of the sums of operators in Banach spaces, we prove that the solution admits a decomposition into a regular part in and an explicit singular part.
Complexity of primal-dual interior-point algorithm for linear programming based on a new class of kernel functions
In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound, we propose a parameterized version of this function. We show that the complexity result meets the currently best iteration bound for large-update methods by choosing a special value of the parameter. Numerical experiments reveal that the new KFs have better...
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