Year: 2024
Type: article
Abstract: In this paper we establish a new mean field-type formulation to study the problem of prescribing Gaussian and geodesic curvatures on compact surfaces with boundary, which is equivalent to the following Liouville-type PDE with nonlinear Neumann conditions: [Formula: see text] The underlying problem allows the application of straightforward variational techniques. Consequently, we provide three different existence results in the cases of positive, zero and negative Euler characteristics by means of variational techniques.
Authors: Luca Battaglia, Rafael López–Soriano
Institutions: Roma Tre University, Universidad de Granada
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1175115578, G1622782223, G210041235, G2262748287, G2473898077, G2601397997, G300979063, G34346518, G3480869486, G3681454997, G4042783231, G410571670, G425668148, G451917667, G5080475149, G5195188938, G5339074417, G5456286744, G5539308778, G5948660273, G5967599077, G66099019, G6841463731, G7084143925, G929308097
OpenAlex ID: W4404164974