Abstract
In 1957, E. De Giorgi [7] solved the 19th Hilbert problem by proving the regularity and analyticity of variational (“energy minimizing weak”) solutions to nonlinear elliptic variational problems. In so doing, he developed a very geometric, basic method to deduce boundedness and regularity of solutions to a priori very discontinuous problems. The essence of his method has found applications in homogenization, phase transition, inverse problems, etc.
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Caffarelli, L.A., Vasseur, A. (2012). The De Giorgi Method for Nonlocal Fluid Dynamics. In: Nonlinear Partial Differential Equations. Advanced Courses in Mathematics - CRM Barcelona. Springer, Basel. https://doi.org/10.1007/978-3-0348-0191-1_1
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