Non-uniformly elliptic equations with natural growth in the gradient
Existence of bounded solutions for a class of nonlinear elliptic problems of type \[ -\text{div\,} (a(x,u,Du))=H(x,u,Du) +f,\qquad u\in W^{1,p}_0(\Omega)\cap L^\infty(\Omega), \] where \(\langle a(x,\eta,\xi),\xi\rangle\geq b(| \eta| )| \xi| ^p,\) \(b\) is a continuous monotone decreasing function and \(| H(x,\eta,\xi)| \leq k(\eta)| \xi| ^p,\) \(k\) is a continuous monotone increasing function, is proved.
scientific article; zbMATH DE number 1901245