Besov estimates for the weak solutions of a class of quasilinear elliptic equations

Besov estimates for weak solutions of a class of quasilinear parabolic equations with general growth

“…The following proposition describes some elementary properties of the functions 𝑎 and 𝐴, whose proofs can be found in Lemma 3 of [31]. Moreover, the proofs can also follow from the change of variables and Lemma 2.3 in [49]. Lemma 2.2.…”

“…The following proposition describes some elementary properties of the functions a and A , whose proofs can be found in Lemma 3 of [31]. Moreover, the proofs can also follow from the change of variables and Lemma 2.3 in [49]. Lemma Assume that $$a(t)$$ satisfies Equation (1.2), $$ A(x, t)$$ satisfies Equation (1.3) and $$V(\xi )$$ is defined in Equation (1.21).…”

“…Inspired by the above papers, in this work we want to prove the corresponding regularity estimates in Besov spaces of weak solutions for the parabolic case (1.1). Essentially, this paper is a natural follow‐up to the papers [3, 6, 23, 34, 35] and our previous paper [49].…”

“…At the same time, many authors [22, 26, 27, 29, 38, 39, 43, 45] also studied regularity estimates in Besov spaces for various types of linear and nonlinear partial differential equations. More recently, we [49] obtained the local regularity estimates in Besov spaces of weak solutions for a class of quasilinear elliptic equations $$$$\begin{eqnarray*} \text{div} \nobreakspace \! {\left(a {\left({\left| \nabla u \right|} \right)} \nabla u \right)}=\text{div}\nobreakspace \mathbf {F} \quad \mbox{in}\nobreakspace \Omega.$$…”

“…At the same time, many authors [22,26,27,29,38,39,43,45] also studied regularity estimates in Besov spaces for various types of linear and nonlinear partial differential equations. More recently, we [49] obtained the local regularity estimates in Besov spaces of weak solutions for a class of quasilinear elliptic equations div(𝑎(|∇𝑢|)∇𝑢) = div 𝐅 in Ω.…”