Proves existence of minimizers together with optimal Lipschitz regularity of the functions and analytic regularity of the free boundaries away from a codimension-2 singular set for two semilinear variational problems with topological constraints.
Partial analyticity and nodal sets for nonlinear elliptic systems
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abstract
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions to the 2-d Euler equation, and analyticity of water waves with and without surface tension.
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math.AP 1years
2024 1verdicts
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Free boundary regularity for semilinear variational problems with a topological constraint
Proves existence of minimizers together with optimal Lipschitz regularity of the functions and analytic regularity of the free boundaries away from a codimension-2 singular set for two semilinear variational problems with topological constraints.