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Journal of Elliptic and Parabolic Equations

, Volume 4, Issue 1, pp 107–139 | Cite as

Solutions of nonlinear equations of divergence type in domains having corner points

  • E. E. Perepelkin
  • B. I. Sadovnikov
  • N. G. Inozemtseva
Article

Abstract

An algorithm has been suggested for finding exact solutions of a nonlinear equation in partial derivatives of a divergence type which appears in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schrödinger equation). The properties of smoothness of solutions in domains with corner points (piecewise smooth boundary) have been considered. The solutions with unbounded derivatives in the corner point domain have been presented on the basis of a new class of special functions.

Keywords

Rigorous result Exact solution Nonlinear equations in partial derivatives Corner point Magnetostatics problem Equation of a divergent type Special functions 

Mathematical Subject Classification

35J15 35J25 35J60 35C10 35Q61 

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Copyright information

© Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • E. E. Perepelkin
    • 1
  • B. I. Sadovnikov
    • 1
  • N. G. Inozemtseva
    • 2
  1. 1.Faculty of PhysicsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Dubna State UniversityMoscowRussia

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