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Regularity Bootstrapping for fourth order nonlinear equations

Arunima Bhattacharya
Tuesday, November 26, 2019 - 1:30pm
PDL C-401

We consider nonlinear fourth order elliptic equations of double divergence type. We show that for a certain class of equations where the nonlinearity is in the Hessian, solutions that are \$C^{2,\alpha}\$ enjoy interior estimates on all derivatives. We then use this result to prove a regularity result for the Lagrangian Hamiltonian stationary equation. 

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