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On a Generalized Prandtl-Batchelor Free Boundary Problem with a Singularity on a Stratified Lie Group (2501.04033v1)
Published 1 Jan 2025 in math.AP
Abstract: We investigate a class of elliptic free boundary problems, including a generalized Prandtl Batchelor type problem with a singularity on a stratified Lie group. The associated energy functional is nondifferentiable, which precludes the direct application of standard variational techniques. Our analysis combines elliptic regularity theory with the mountain pass theorem in a non-Euclidean setting
