Journal
NONLINEARITY
Volume 32, Issue 7, Pages 2481-2495Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/ab0b03
Keywords
Baouendi-Grushin operator; Caffarelli-Kohn-Nirenberg inequality; transonic flow; nonlinear eigenvalue problem; variable exponent Mathematics Subject Classification numbers: Primary: 35J70; Secondary: 35P30; 76H05
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Funding
- Slovenian Research Agency [P1-0292, J1-8131, J1-7025, N1-0064, N1-0083]
- DGISPI (Spain) [MTM2017-85449-P]
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In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. After establishing a weighted inequality for the Baouendi-Grushin operator and a related compactness property, we establish the existence of stationary waves under arbitrary perturbations of the reaction.
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