We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. {-Δu=2K(z)euinD2,∂νu+2=2h(z)eu2on∂D2,where K, h are the prescribed curvatures. We construct a family of conformal metrics with curvatures Kε, hε converging to K, h respectively as ε goes to 0, which blows up at one boundary point under some generic assumptions.
Battaglia, L., Medina, M., & Pistoia, A. (2021). Large conformal metrics with prescribed Gaussian and geodesic curvatures. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(1).
Titolo: | Large conformal metrics with prescribed Gaussian and geodesic curvatures |
Autori: | |
Data di pubblicazione: | 2021 |
Rivista: | |
Citazione: | Battaglia, L., Medina, M., & Pistoia, A. (2021). Large conformal metrics with prescribed Gaussian and geodesic curvatures. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(1). |
Handle: | http://hdl.handle.net/11590/380327 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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