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math.AP2019
A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth
Gabrielle Nornberg, Delia Schiera, Boyan Sirakov
We consider fully nonlinear uniformly elliptic cooperative systems with quadratic growth in the gradient, such as $$ -F_i(x, u_i, Du_i, D^2 u_i)- \langle M_i(x)D u_i, D u_i \rangle…
math.AP2019
A new method of proving a priori bounds for superlinear elliptic PDE
Boyan Sirakov
We describe a new method of proving a priori bounds for positive supersolutions and solutions of superlinear elliptic PDE, based on global weak Harnack inequalities and a quantitat…