| 1. |
- Avdonin, Sergey, et al.
(författare)
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Stability estimate for an inverse problem in glaciology
- 2012
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Ingår i: Analysis and Mathematical Physics. - Basel : Birkhäuser Verlag. - 1664-2368 .- 1664-235X. ; 2:4, s. 367-387
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of reconstruction of the basal velocity of a glacier by measurements of the velocity on glacier’s surface. The main result is a stability estimate in a near-surface region, which represents a multiplicative inequality and shows that small errors in measurements produce small errors in the velocity in this region.
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| 2. |
- Gustafsson, Björn, 1947-, et al.
(författare)
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On the curvature of some free boundaries in higher dimensions
- 2012
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Ingår i: Analysis and Mathematical Physics. - : Springer. - 1664-2368 .- 1664-235X. ; 2, s. 247-275
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Tidskriftsartikel (refereegranskat)abstract
- It is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition, in other words there is a specific upper bound on the curvature of the boundary. This result directly applies to free boundaries appearing in obstacle type problems and in Hele-Shaw flow. In the present paper we make partial progress on the corresponding question in higher dimensions. Specifically, we prove the equivalence between several different ways to formulate the inner ball condition, and we compute the Brouwer degree for a geometrically important mapping related to the Schwarz potential of the boundary. The latter gives in particular a new proof in the two dimensional case.
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| 3. |
- Hoppe, Jens, et al.
(författare)
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Diffeomorphism algebra structure and membrane theory
- 2012
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Ingår i: Analysis and Mathematical Physics. - : Springer Science and Business Media LLC. - 1664-2368 .- 1664-235X. ; 2:3, s. 277-283
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Tidskriftsartikel (refereegranskat)abstract
- Explicit structure constants are calculated for Lie algebras of vectorfields on 2-dimensional compact manifolds.
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| 4. |
- Tkachev, Vladimir
(författare)
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A note on isoparametric polynomials
- 2014
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Ingår i: Analysis and Mathematical Physics. - Basel : Springer. - 1664-2368 .- 1664-235X. ; 4:3, s. 237-245
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Tidskriftsartikel (refereegranskat)abstract
- We show that any homogeneous polynomial solution of the eiconal type equation |∇F(x)|2 = m2|x|2m-2, m ≥ 1, is either a radially symmetric polynomial F(x) = ±|x|m (for even values of m’s) or it is a composition of a Chebychev polynomial and a Cartan–Münzner polynomial.
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