Local regularity results for some parabolic equations (Q2716471)

The paper is devoted to prove \(L^s_{\text{loc}}\)-regularity for unbounded weak solutions of nonlinear parabolic equations whose prototype is NEWLINE\[NEWLINEu_t-\text{div}\bigl( |Du|^{p-2} Du\bigr)= -\sum^N_{j=1} {\partial f_j\over \partial x_j} \text{ in }D'(Q_T),\tag{1}NEWLINE\]NEWLINE where \(p>1\), and \(s\) is finite and depends on the local summability of the data \(f_j\), \(Q_T= \Omega \times (0,T)\) with bounded \(\Omega\). The author proves the local \(L^s\) regularity for local ``unbounded'' weak solutions of (1). To this end the author uses a double summation technique whose role is to ``adjust'' the powers in an integral estimate of energy type and an iterative argument that permits to conclude the process in a finite number of steps.