1 citations · 1 across the 7 of their papers we have counts for
9 papers
Time-zero limits of Kaden's spirals and 2D Euler
Bartosz Bieganowski, Tomasz Cieślak, Jakub Siemianowski
The present note is devoted to the studies of the relation of the time-zero limits of Kaden's spirals and the 2D Euler equation. It is shown that the time-zero limits of Kaden's sp…
Brezis--Kato Type Regularity Results for Higher Order Elliptic Operators
Jakub Siemianowski
We prove a Brezis--Kato regularity type results for solutions of the higher order nonlinear elliptic equation \[ L u = g(x,u)\qquad\text{in }Ω\] with an elliptic operator of $2…
Magnetostatic levitation and two related linear PDEs in unbounded domains
Bartosz Bieganowski, Tomasz Cieślak, Jakub Siemianowski
We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a sol…
Biharmonic nonlinear scalar field equations
Jarosław Mederski, Jakub Siemianowski
We prove a Brezis-Kato-type regularity result for weak solutions to the biharmonic nonlinear equation with a Carathéodory function $…
Existence of viscosity solutions with the optimal regularity of a two-peakon Hamilton--Jacobi equation
Tomasz Cieślak, Jakub Siemianowski
This work is devoted to the studies of a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian, which comes from the dynamics of a multipeakon in the Camassa--Holm…
Viscosity solutions to an initial value problem for a Hamilton--Jacobi equation with a degenerate Hamiltonian occurring in the dynamics of peakons
Tomasz Cieślak, Jakub Siemianowski, Andrzej Święch
We consider an initial value problem for a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian. Our Hamiltonian comes from the dynamics of -peakon in the Camas…
Constrained Semilinear Elliptic Systems on
Wojciech Kryszewski, Jakub Siemianowski
We prove the existence of solutions in of the following strongly coupled semilinear system of second order elliptic PDEs on \[ \…
The Bolzano mean-value theorem and partial differential equations
Wojciech Kryszewski, Jakub Siemianowski
We study the existence of solutions to abstract equations of the form , , where A is an abstract differential operator acting in a Banach space ,…
The Constrained Krasnosel'skii Formula for Parabolic Differential Inclusions
Wojciech Kryszewski, Jakub Siemianowski
We consider a constrained evolution inclusions of parabolic type \eqref{inkluzja-rozn} involving an -dissipative linear operator and the source term of multivalued type in a Ban…