Related papers: Inequalities in problems on non-overlapping domain…
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
We present how to obtain non-comparable regular but not completely regular spaces. We analyze a generalization of Mysior's example, extracting its underlying purely set-theoretic framework. This enables us to build simple counterexamples,…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a…
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular $k$-gons. For $n\le 4$ we determine formulas for the number $a_k(n)$ of generalized polyominoes consisting of $n$ regular $k$-gons.…
This paper deals with the lack of compactness in nonlinear elliptic problems $(P)$. In particular, a domain $\Omega$ is provided where not converging Palais-Smale sequences exist at every energy level. Nevertheless, it is proved that…
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
A set of real $n$th roots that is pairwise linearly independent over the rationals must also be linearly independent. We show how this result may be extended to more general fields.
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
The aim of this note is to present an alternative proof for an already known result relative to the solvability of the Dirichlet problem in Riemannian manifolds (see remark 0.1). In particular, we discuss the p-regularity (regularity…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
This paper concerns the boundary behavior of solutions of certain fully nonlinear equations with a general drift term. We elaborate on the non-homogeneous generalized Harnack inequality proved by the second author in (Julin, ARMA -15), to…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
We extend our discrete uniformization theorems for planar, $m$-connected, Jordan domains [Journal f\"ur die reine und angewandte Mathematik 670 (2012), 65--92] to closed surfaces of non-positive genus.
Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove…
We establish point wise inequalities for Sobolev functions on a wider class of outward cuspidal domains. It is a generalization of an earlier result by the author and his collaborators