3 papers
math.AP2021
Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume
Kathrin Stollenwerk
We formulate the minimization of the buckling load of a clamped plate as a free boundary value problem with a penalization term for the volume constraint. As the penalization param…
math.AP2021
On the optimal domain for minimizing the buckling load of a clamped plate
Kathrin Stollenwerk
We prove the existence of an optimal domain for minimizing the buckling load among all, possibly unbounded, open subsets of () with given measure. Our appro…
math.AP2021
Existence of an optimal domain for minimizing the fundamental tone of a clamped plate of prescribed volume in arbitrary dimension
Kathrin Stollenwerk
In the 19th century, Lord Rayleigh conjectured that among all clamped plates with given area, the disk minimizes the fundamental tone. In the 1990s, N. S. Nadirashvili proved the c…