We are interested in variational problems of the form min ∝W(∇u) dx, with W nonconvex. The theory of relaxation allows one to calculate the minimum value, but it does not determine a well-defined "solution" since minimizing sequences are far from unique. A natural idea for determining a solution is regularization, i.e. the addition of a higher order term such as ε|∇∇u|2. But what is the behavior of the regularized solution in the limit as ε→0? Little is known in general. Our recent work [19, 20, 21] discusses a particular problem of this type, namely min u y=±1 ∝∝u x 2 +ε|u yy|dxdy with various boundary conditions. The present paper gives an expository overview of our methods and results.
|Original language||English (US)|
|Number of pages||25|
|Journal||Rendiconti del Seminario Matematico e Fisico di Milano|
|State||Published - Dec 1992|
ASJC Scopus subject areas
- Physics and Astronomy(all)