Pointwise Bounds in the Cauchy problem of elastic plates
Lawrence Edward Payne · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · 1961
Let an elastic plate occ up y a region D wit h boundary C. On a p orti on ~ of C t he defle ction, slop e, m ome nt, and s hear are m easured.In terms of t hese data, and crud e bounds for the maximum defl ection and mom ent, pointwise bounds for t he valu e of t he deflection and its der ivatives in D a re obtained.These bounds are such that if t he data on ~ and the loa ding p erpendi cular to the plane of the plate te nd to ze ro, t he defl cction tends to zero at ever y point in D. Sim ilar bo unds a re obtain ed in the slow fl ow proble m for a viscous fluid .