1,721,017 research outputs found
Three dimensional Bonnesen type inequalities
No full textA well-known result in convex geometry proved by Favard states that among all convex plane sets of given perimeter and area, the symmetric lens is the unique element of maximum circumradius. In this note a new proof of Favard’s theorem is exhibited and possible extensions in higher dimensions are discussed
Isoperimetric deficit and convex plane sets of maximum translative discrepancy
No full textThe paper deals with the following question: Among the convex plane sets of fixed isoperimetric deficit, which are the sets of maximum translative deviation from the circular shape? The answer is given for the cases in which the deviation is measured either by the translative Hausdorff metric or by the translative symmetric difference metric
Stability estimates for star bodies in terms of their intersection bodies
No full textThe paper deals with the problem of estimating the distance, in radial or Hausdorff metrics, between two centred star bodies of R^d in terms of the distance between the corresponding intersection bodies. Stability estimates are obtained, under suitable restrictions on the size of the bodies
On the exterior Dirichlet problem for linear elliptic equations in the plane
No full textIn this paper the exterior Dirichlet problem for linear elliptic equations in two independent variables with bounded measurable coefficients is investigated. An existence-uniqueness theorem is established in a suitably weighted Sobolev class. Some a-priori estimates are derived. © 1979 Fondazione Annali di Matematika Pura ed Applicata
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