On solvability of elliptic boundary value problems via global invertibility

• Autorzy: Bełdziński Michał , Galewski Marek

Identyfikatory

DOI

10.7494/OpMath.2020.40.1.37

• Języki publikacji: EN

Abstrakty

EN

In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.

Słowa kluczowe

EN

diffeomorphism; Dirichlet conditions; Laplace operator; Neumann conditions; uniqueness

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2020
• Tom: Vol. 40, no. 1
• Strony: 37--47
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Bełdziński Michał

• Lodz University of Technology Institute of Mathematics Wólczańska 215, 90-924 Łódź, Poland

autor

Galewski Marek

• Lodz University of Technology Institute of Mathematics Wólczańska 215, 90-924 Łódź, Poland

Bibliografia

• [1] A. Ambrosetti, G. Prodi, A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics, vol. 34, Cambridge University Press, 1995.
• [2] M. Bełdziński, M. Galewski, Global diffeomorphism theorem applied to the solvability of discrete and continuous boundary value problems, J. Difference Equ. Appl. 24 (2018) 2, 277-290.
• [3] M. Bełdziński, M. Galewski, R. Stegliński, Solvability of abstract se.miline.ar equations by a global diffeomorphism theorem, Result. Math. 73 (2018) 3, Paper No. 122.
• [4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, New York, Springer, 2011.
• [5] D. Idczak, A. Skowron, S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Adv. Nonlinear Stud. 12 (2012) 1, 89-100.
• [6] K. Schmudgen, Unbounded Self-adjoint Operators on Hilbert Space, Graduate Texts in Mathematics, vol. 265, Springer, Dordrecht, 2012.
• [7] R. Stegliński, A global diffeomorphism theorem and a unique weak solution of Dirichlet problem, Complex Var. Elliptic Equ. 64 (2019) 8, 1285-1296.
• [8] E. Zeidler, Nonlinear Functional Analysis and its Applications. I: Fixed-point Theorems, New York, Springer-Verlag, 1986.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).