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We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on… Click to show full abstract
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry, results for solutions to overdetermined problems on Riemannian manifolds of nonconstant curvature.
Keywords:
equations position;
overdetermined boundary;
dependent nonlinearities;
position dependent;
semilinear equations;
solutions overdetermined
Journal Title: Advances in Mathematics
Year Published: 2019
Link to full text (if available)
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Journal Title: Advances in Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!