## Local gradient estimates and existence of blow-up solutions to a class of quasilinear elliptic equations.(English)Zbl 1284.35190

From the introduction: In this paper we study the existence of minimal and maximal positive blow-up solutions, that is $\lim_{_{\substack{ \text{dist}(x,\partial\Omega)\to 0,\\ x\in\Omega}}}u(x)=+\infty,$ to the quasilinear elliptic equation $-\Delta u+ H(x,u,\nabla u) = f\quad\text{in}\;\Omega, \tag{1}$ where $$\Omega$$ is a smooth bounded domain, $$f\in L^\infty_{\text{loc}}(\Omega)$$, and $$H$$ is an appropriate function.

### MSC:

 35J62 Quasilinear elliptic equations 35B45 A priori estimates in context of PDEs 35B44 Blow-up in context of PDEs
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### References:

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