Abstract
We consider the solution u to a semilinear elliptic boundary value problem with Dirichlet boundary condition on an annular planar domain with corners. We prove that u possesses a finite number of critical points and at most one critical curve. For certain annular domains having a regular n–gon as an outer boundary, we rule out the existence of critical curves.
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Acknowledgment
The authors thank El Posgrado en Ciencias Matemáticas de la Universidad del Valle for providing the financial support and the academic environment to carry out this research. J. Delgado thanks the organizing committee of ICAMI 2013 for allowing him to present these results in the ICAMI meeting. J. Arango is greatly indebted to D. Cabarcas for her collaborations in proving Theorem 3 and for many stimulating conversations.
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Arango, J., Delgado, J. (2015). Critical Points of Solutions to Elliptic Equations in Planar Domains with Corners. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_7
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DOI: https://doi.org/10.1007/978-3-319-12583-1_7
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