FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2284557637> ?p ?o ?g. }

• W2284557637 endingPage "256" @default.
• W2284557637 startingPage "239" @default.
• W2284557637 abstract "In this paper we prove the existence of nonparametric minimal surfaces of annulus type spanning boundary configurations (Γ ,S) where S is a vertical cylinder above a simple closed polygon P (S) in the x, y-plane and the surrounding Jordan curve Γ is given as a generalized graph above its convex projection curve P (Γ ) (cf. Corollary 1). The behaviour of such minimal surfaces at the edges of the support surface is of special interest. The case of more general support surfaces S where P (S) merely is a closed piecewise smooth Jordan curve can be treated by approximation. The nonparametric existence problem is by no means trivial. For instance, concerning the pure Dirichlet problem for the nonparametric minimal surface equation on a nonconvex Jordan domain Ω, there are always (arbitrary small) boundary values on ∂Ω for which the problem is not solvable. This result of Jenkins and Serrin can be found in the literature, see, e.g., [21, §411]. We have assumed P (Γ ) to be convex, but we try to solve the nonparametric minimal surface equation on the doubly connected domain G bounded by P (Γ ) and P (S), i.e., on a domain with a hole. Moreover we have a mixed boundary condition. In [20] T. Nehring proved the existence of an embedded parametric minimal surface with a Jordan curve Γ lying above a circle as fixed boundary and with a free boundary on a smooth surface F which bounds a compact, strictly convex body. In contrast to that paper we do not have to impose any convexity condition on the cylinder surface S. Finally, the support surface S is singular because we allow S to have edges. In the forthcoming paper [27] it will be shown that the free trace of a minimal surface spanning (Γ ,S) need not have a 1–1-projection into the x, y-plane. The free trace can attach to an edge of S in a full interval. This phenomenon is called edge-creeping. Apparently this phenomenon was discovered by Y.W. Chen when treating an exterior free boundary value problem for minimal surfaces (cf. [4]). There the support surface is a vertical cylinder above a closed convex polygon. Later S. Hildebrandt and J.C.C. Nitsche in [8] proved existence and optimal regularity of solutions to a partially free boundary value problem where edge-creeping occurs. A semifree problem for disc-type minimal surfaces with singular boundaries has been discussed in joint work of S. Hildebrandt and F. Sauvigny [12–14]. They choose the support surface S as the boundary of a wedge, or, more generally, as a polyhedral cylinder surface, and Γ is assumed to be a smooth Jordan arc with its endpoints on S. In [12] asymptotic expansion formulas for the derivatives Xw and Nw of the minimal surface X and its Gauss map N are proved, which can easily be transferred to the doubly connected case. In [14] an existence theorem for embedded minimal surfaces of disc type is given. This is achieved by combining the results of [11], obtained in the case of smooth boundaries, and [12] with a suitable" @default.
• W2284557637 created "2016-06-24" @default.
• W2284557637 creator A5020769677 @default.
• W2284557637 date "2000-01-01" @default.
• W2284557637 modified "2023-09-23" @default.
• W2284557637 title "Existence of doubly connected minimal graphs in singular boundary configurations" @default.
• W2284557637 cites W1509577866 @default.
• W2284557637 cites W1509891962 @default.
• W2284557637 cites W1606550863 @default.
• W2284557637 cites W1970108908 @default.
• W2284557637 cites W1972935357 @default.
• W2284557637 cites W1973265947 @default.
• W2284557637 cites W1987420620 @default.
• W2284557637 cites W1999981977 @default.
• W2284557637 cites W2046062975 @default.
• W2284557637 cites W2048403746 @default.
• W2284557637 cites W2050622374 @default.
• W2284557637 cites W2069162038 @default.
• W2284557637 cites W2072791498 @default.
• W2284557637 cites W2077819608 @default.
• W2284557637 cites W2088463128 @default.
• W2284557637 cites W2092047840 @default.
• W2284557637 cites W2154973461 @default.
• W2284557637 cites W2325505781 @default.
• W2284557637 cites W375411588 @default.
• W2284557637 cites W395050932 @default.
• W2284557637 hasPublicationYear "2000" @default.
• W2284557637 type Work @default.
• W2284557637 sameAs 2284557637 @default.
• W2284557637 citedByCount "1" @default.
• W2284557637 crossrefType "journal-article" @default.
• W2284557637 hasAuthorship W2284557637A5020769677 @default.
• W2284557637 hasConcept C106159729 @default.
• W2284557637 hasConcept C112680207 @default.
• W2284557637 hasConcept C114614502 @default.
• W2284557637 hasConcept C134306372 @default.
• W2284557637 hasConcept C162324750 @default.
• W2284557637 hasConcept C167204820 @default.
• W2284557637 hasConcept C182310444 @default.
• W2284557637 hasConcept C2524010 @default.
• W2284557637 hasConcept C2776799497 @default.
• W2284557637 hasConcept C2779560616 @default.
• W2284557637 hasConcept C30707913 @default.
• W2284557637 hasConcept C33923547 @default.
• W2284557637 hasConcept C34388435 @default.
• W2284557637 hasConcept C36503486 @default.
• W2284557637 hasConcept C45340560 @default.
• W2284557637 hasConcept C62354387 @default.
• W2284557637 hasConcept C70251129 @default.
• W2284557637 hasConcept C72134830 @default.
• W2284557637 hasConceptScore W2284557637C106159729 @default.
• W2284557637 hasConceptScore W2284557637C112680207 @default.
• W2284557637 hasConceptScore W2284557637C114614502 @default.
• W2284557637 hasConceptScore W2284557637C134306372 @default.
• W2284557637 hasConceptScore W2284557637C162324750 @default.
• W2284557637 hasConceptScore W2284557637C167204820 @default.
• W2284557637 hasConceptScore W2284557637C182310444 @default.
• W2284557637 hasConceptScore W2284557637C2524010 @default.
• W2284557637 hasConceptScore W2284557637C2776799497 @default.
• W2284557637 hasConceptScore W2284557637C2779560616 @default.
• W2284557637 hasConceptScore W2284557637C30707913 @default.
• W2284557637 hasConceptScore W2284557637C33923547 @default.
• W2284557637 hasConceptScore W2284557637C34388435 @default.
• W2284557637 hasConceptScore W2284557637C36503486 @default.
• W2284557637 hasConceptScore W2284557637C45340560 @default.
• W2284557637 hasConceptScore W2284557637C62354387 @default.
• W2284557637 hasConceptScore W2284557637C70251129 @default.
• W2284557637 hasConceptScore W2284557637C72134830 @default.
• W2284557637 hasLocation W22845576371 @default.
• W2284557637 hasOpenAccess W2284557637 @default.
• W2284557637 hasPrimaryLocation W22845576371 @default.
• W2284557637 hasRelatedWork W1963952373 @default.
• W2284557637 hasRelatedWork W1984097905 @default.
• W2284557637 hasRelatedWork W1999657356 @default.
• W2284557637 hasRelatedWork W2041716313 @default.
• W2284557637 hasRelatedWork W2043412112 @default.
• W2284557637 hasRelatedWork W2067025278 @default.
• W2284557637 hasRelatedWork W2092047840 @default.
• W2284557637 hasRelatedWork W2113710381 @default.
• W2284557637 hasRelatedWork W2154973461 @default.
• W2284557637 hasRelatedWork W2168899702 @default.
• W2284557637 hasRelatedWork W2198318189 @default.
• W2284557637 hasRelatedWork W2323972483 @default.
• W2284557637 hasRelatedWork W241049422 @default.
• W2284557637 hasRelatedWork W2501838022 @default.
• W2284557637 hasRelatedWork W2554683451 @default.
• W2284557637 hasRelatedWork W2591958460 @default.
• W2284557637 hasRelatedWork W2956874061 @default.
• W2284557637 hasRelatedWork W3199466712 @default.
• W2284557637 hasRelatedWork W3788551 @default.
• W2284557637 hasRelatedWork W96661133 @default.
• W2284557637 hasVolume "23" @default.
• W2284557637 isParatext "false" @default.
• W2284557637 isRetracted "false" @default.
• W2284557637 magId "2284557637" @default.
• W2284557637 workType "article" @default.