Rotation-free solutions with positive infimum of the equation ...u = Pu in a neighbourhood of a singularity of the density P.
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Szegő projections for Hardy spaces of monogenic functions and applications.
The current situation in the linear problem of Molodenskii
Si prova l'esistenza di un'unica soluzione debole che dipende con continuità dai dati al contorno per il problema lineare di Molodenskii in approssimazione quasi sferica, nel caso che la superficie al contorno soddisfi una condizione di cono. Si segue un approccio costruttivo diretto, che generalizza una procedura precedentemente elaborata per il problema semplice di Molodenskii. Inoltre si prova che la soluzione ha derivate prime a quadrato integrabile al contorno, il che è essenziale per le applicazioni...
The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected domains.
The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves.
The transmission problem with boundary conditions given by real measures
The unique solvability of the problem Δu = 0 in G⁺ ∪ G¯, u₊ - au_ = f on ∂G⁺, n⁺·∇u₊ - bn⁺·∇u_ = g on ∂G⁺ is proved. Here a, b are positive constants and g is a real measure. The solution is constructed using the boundary integral equation method.
Third boundary value problem for the heat equation. II.
Two-dimensional problems of elasticity of anisotropic bodies.
Ueber die Randwertaufgabe für eine ebene Randcurve mit stückweise stetig sich ändernden Tangenten und ohne Spitzen
Uniqueness and Free Interpolation for Logarithmic Potentials and the Cauchy Problem for the Laplace Equation in R2.
Uniqueness of Dirichlet, Neumann, and mixed boundary value problems for Laplace's and Poisson's equations for a rectangle.
Wiener's type regularity criteria on the complex plane
We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is Hölder continuous....
Zur Holomorphie des Poissonintegrals.
Исключительный случай задачи Римана в пространстве обобщенных функций
К обратной задаче логарифмического потенциала
О краевой задаче Неймана в области со сложной границей
О множествах единственности гармонических функций в единичном круге
О разрешимости в "малом" обратной задачи потенциала с переменной плотностью в двумерном случае.
О характере непрерывности на границе негладкой области обобщенного решения задачи Дирихле для бигармонического уравнения