We study the oblique derivative problem for uniformly elliptic equations on cone domains. Under assumption of axi-symmetry solution, we find sufficient conditions angle vector Hölder regularity gradient to hold up vertex cone. The proof is based application carefully constructed barrier methods or via perturbative arguments. In case that such does not hold, give explicit counterexamples. also a...

The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary la...

We show that time-reflection symmetric, asymptotically flat, static vacuum data which admit a non-trivial conformal rescaling which leads again to such data must be axi-symmetric and admit a conformal Killing field. Moreover, it is shown that there exists a 3-parameter family of such data. PACS: 04.20.Ex, 04.20.Ha, 04.20.Jb

We show that time-reflection symmetric, asymptotically flat, static vacuum data which admit a non-trivial conformal rescaling which leads again to such data must be axi-symmetric and admit a conformal Killing field. Moreover, it is shown that there exists a 3-parameter family of such data. PACS: 04.20.Ex, 04.20.Ha, 04.20.Jb

The paper presents a methodology of computer modelling of continual surface induction hardening of axi-symmetric bodies. The body is heated by a cylindrical inductor moving at a given velocity along it and the heated part is then cooled by spraying water. While the mathematical model of induction heating is given by two partial differential equations describing the harmonic electromagnetic and ...