A saint-venant principle for the gradient in the Neumann problem

Wheeler, Lewis; Turteltaub, M. J.; Horgan, Cornelius O.

doi:10.1007/bf01591502

Cited by 10 publications

(3 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The work described here generalizes the results in [4], which treats by similar methods the same problem for Laplace's equation on a curved strip. In [4] we made essential use of the fact that if u is harmonic then |V«|2 is subharmonic.…”

Section: Introductionmentioning

confidence: 66%

“…In the present paper, we have benefited from results given in a recent paper [5] by Protter and Weinberger, which furnish a suitable counterpart of this property for the operator L. Another key element in this generalization process is Littman's work in [6] on weakly L-subharmonic functions, which greatly facilitated the construction of a certain auxiliary function by easing the burden of smoothness requirements. The increased generality of the present results over [4] broadens their application to include the axisymmetric torsion of shells of uniform thickness and the axisymmetric potential flow of fluids in regions of the same geometry.1 2. Gradient bounds for the sides and far end.…”

Section: Introductionmentioning

confidence: 77%

“…In [4] we made essential use of the fact that if u is harmonic then |V«|2 is subharmonic. In the present paper, we have benefited from results given in a recent paper [5] by Protter and Weinberger, which furnish a suitable counterpart of this property for the operator L. Another key element in this generalization process is Littman's work in [6] on weakly L-subharmonic functions, which greatly facilitated the construction of a certain auxiliary function by easing the burden of smoothness requirements.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A two-dimensional Saint-Venant principle for second-order linear elliptic equations

Wheeler¹,

Horgan²

1976

Quart. Appl. Math.

Self Cite

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A two-dimensional Saint-Venant principle for second-order linear elliptic equations

Wheeler¹,

Horgan²

1976

Quart. Appl. Math.

Self Cite

View full text Add to dashboard Cite

Maximum principles and pointwise error estimates for torsion of shells of revolution

Horgan

Wheeler

1977

J Elasticity

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the question of assessing the quality of approximate thin shell solutions for the problem of axisymmetric torsion of elastic shells of revolution, an issue previously considered by Ho and Knowles [1]. In both works, the objective is to obtain pointwise estimates, based on the threedimensional theory of elasticity, for the errors involved in using an approximate shell theory.The mathematical problem is that of obtaining explicit pointwise gradient estimates for the solutions of homogeneous and nonhomogeneous second-order uniformly elliptic equations, an issue of interest beyond the present context. In contrast to arguments using energy inequalities, here we apply a technique based on maximum principles for such equations.The particular examples of cylindrical, spherical and conical shells of revolution are discussed in detail. In the former two cases, it is shown that the shell theory solution is in fact an exact elasticity solution in the Saint-Venant sense. Asymptotic error estimates for general shells of revolution are also given. RI~SUMIEL'6tude qi-dessous traite de la qualit6 de l'approximation des coques minces appliquEe aux probl~mes de torsion asym6trique des coques 61astiques de r6volution, probl6me d6j~ consid6r6 par Ho et Knowles [1].L'objectif des deux 6tudes est d'6valuer en chaque point, par la th6orie de l'61asticit6 en trois dimensions, les erreurs cons6quentes h l'utilisation de la th6orie de l'approximation des coques.Le probl~me math6matique consiste h obtenir une estimation explicite en chaque point des gradients pour les solutions d'6quations elliptiques uniformes du deuxi~me ordre, homog~nes et non-homog6nes, probl~me d'un inter& qui d6passe le pr6sent contexte. Nous utilisons ici une technique bas6e sur le principe du maximum pour de telles 6quations, par contraste avec les raissonnements utilisant des in6galit6s 6nerg6tiques.Les exemples particuliers des coques de r6volution cylindriques, sph6riques et coniques sont discut6s en d6tail. Dans les deux premiers cas, nous montrons que la solution par la th6orie des coques est en fait une solution exacte dans le sens de Saint-Venant. Des estimations asymptotiques des erreurs dans le cas de coques de r6volution plus g6n6rales sont 6galement donn6es.

show abstract

Spatial decay estimates for the heat equation via the maximum principle

Horgan

Wheeler

1976

Journal of Applied Mathematics and Physics (ZAMP)

View full text Add to dashboard Cite

A saint-venant principle for the gradient in the Neumann problem

Cited by 10 publications

References 4 publications

A two-dimensional Saint-Venant principle for second-order linear elliptic equations

A two-dimensional Saint-Venant principle for second-order linear elliptic equations

Maximum principles and pointwise error estimates for torsion of shells of revolution

Spatial decay estimates for the heat equation via the maximum principle

Contact Info

Product

Resources

About