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Published in:
2012 | OriginalPaper | Chapter
The De Giorgi Method for Nonlocal Fluid Dynamics
Authors : Luis A. Caffarelli, Alexis Vasseur
Published in: Nonlinear Partial Differential Equations
Publisher: Springer Basel
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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.