Limits as p ( x ) → ∞ of p ( x ) -harmonic functions

Limits as p ( x ) → ∞ of p ( x ) -harmonic functions

In this note we study the limit as p ( x ) → ∞ of solutions to − Δ p ( x ) u = 0 in a domain Ω , with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to + ∞ and analyzing how the corresponding solutions of the problem converge...

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Veröffentlicht in:Nonlinear analysis 2010, Vol.72 (1), p.309-315
Hauptverfasser: Manfredi, J.J., Rossi, J.D., Urbano, J.M.
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-Laplacian
Calculus of variations and optimal control
Exact sciences and technology
Infinity Laplacian
Mathematical analysis
Mathematics
Sciences and techniques of general use
Variable exponents
Viscosity solutions
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Zusammenfassung:In this note we study the limit as p ( x ) → ∞ of solutions to − Δ p ( x ) u = 0 in a domain Ω , with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to + ∞ and analyzing how the corresponding solutions of the problem converge and which equation is satisfied by the limit.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.06.054