Existence and regularity results for nonlinear parabolic equations with quadratic growth with respect to the gradient

On some regularity results of parabolic problems with nonlinear perturbed terms and general data

“…A natural question is whether conditions on m are still necessary for parabolic problems when considering different classes of initial/measure data. Finally, note that, for a(t, x) and b(t, x) are measurable positive functions, some new results have been obtained, in [60], for the model problems…”

On nonlinear parabolic equations with singular lower order term

“…Boccardo In [5] has been studied the existence and regularity results of quasi linear elliptic problem where a(x), b(x) are measurable bounded functions, p, q ≥ 0 and 0 ≤ f ∈ L m ( ), 1 ≤ m ≤ N 2 , see also [19]. In the case parabolic the authors in [18] has been studied the existence and regularity results of nonlinear problems where a(x, t), b(x, t) are measurable positive bounded functions, p, q > 0 and f belongs to L m (Q) for some m ≥ 1. If q = 0, then the operator A(x, t, ) = b(x, t) existing in [14] and [8](p = 2 ) is linear coercive, monotone and satisfying the growth condition |A(x, t, )| ≤ C(d(x, t) + | |) with C a positive constant and d ∈ L 2 (Q), we highlight that our case ( q > 0 ) the required growth of A(x, t, s, ) = (a(x, t) + s q ) is more general, handling growths greater then linear case (see also [3,10,15,28]).…”