On three-dimensional vortex patches
On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations.
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On time optimal control of the wave equation, its regularization and optimality system
An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.
On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.
On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique
We generalize to the p-Laplacian Δp a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of Δp of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants. The method of proof...
On total differential inclusions
On trace theorems for pseudo-differential operators
On traces of solutions of a semilinear partial differential equation of elliptic type
On transformations of the Rabelo equations.
On transitive submanifolds of and
On two boundary value problems for mixed type equations with perpendicular lines of type change.
On two classes of weighted Sobolev-Slobodetskiĭ spaces in a dihedral angle
On two methods for the parameter estimation problem with spatio-temporal FRAP data
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
On Two-Dimensional Elliptic Systems with a One-sided Condition.
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.
On two-dimensional hamiltonian transport equations with Llocp coefficients
On Two-Dimensional Quasi-Linear Elliptic Systems.
On two-sided difference methods for ordinary differential equations