Serrin-Type Overdetermined Problems: an Alternative Proof

By B. Brandolini, Carlo Nitsch, Paolo Salani, Cristina Trombetti. 2008

122 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f00b4ccdf8ccc471d471b838a269df91ac0ff8bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Giulio Ciraolo
2. G. Lu
3. Jiuyi Zhu
4. C. Bianchini
5. Sven Jarohs
6. Alessio Figalli
7. A. Roncoroni
8. M. Fall

In Mathematical Physics

1. Giulio Ciraolo
2. C. Bianchini
3. Jiuyi Zhu
4. M. Fall
5. Sven Jarohs
6. A. Roncoroni
7. G. Lu
8. Alessio Figalli

Citations in the corpus

• Wulff shape characterizations in overdetermined anisotropic elliptic problems (2017, methodology): “This approach is new even in the Euclidean case, and it allows us to generalize the results in [9] [10] and [12] to degenerate operators in an anisotropic setting.”
• Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019, result): “It was later shown that both the results of Alexandrov and Serrin can be proved by using an integral approach (see [34, 35, 47] and also [6, 7, 8, 14, 31, 48] where analogous problems are studied in an anisotropic setting and in convex cones).”
• Overdetermined problems with fractional Laplacian (2013, background): “[6, 40] and also [18] which reveal the application of Alexandrov’s result in the study of (1.”
• On the stability of the Serrin problem (2008, background): “Recently yet another proof was given in [ 3 ] where the authors observed that the solutions to Poisson problems are subject to an integral inequality and the equality sign, achieved in case of the overdetermined boundary conditions given above, enforces the solution to be radially”
• The Hadwiger Theorem on Convex Functions, I (2020, unknown): “We start with a lemma which can be found in [9] (see formula (11)).”
• An overdetermined problem in Riesz-potential and fractional Laplacian (2011, result): “s proof relies crucially on the linearity of the Laplace operator. Since the work of [Se], many results are obtained about overdetermined problems. The interested reader may refer to [AB], [B], [BK], [BNST], [BNST1], [CS], [EP], [FG], [FGK], [FK], [FV], [G], [GL], [HPP], [Lim], [Liu], [M], [MR], [PP”