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We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power. [ABSTRACT FROM AUTHOR]

Abstract: Under some assumptions on the continuous function , we obtain the local regularity of solutions of the strong -Laplacian by using the integral estimates in Campanato spaces. [Copyright &y& Elsevier]

Abstract: In this paper we establish a stability result and an error estimate of weak solutions for the initial-boundary value problem of a generalized thin film equation and also obtain some higher regularity results for weak solutions. [Copyright &y& Elsevier]

Abstract: In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a generalized thin film equation. In addition, we present some interesting results on the regularity of weak solutions. [Copyright &y& Elsevier]

In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f ∈ B M O (R n) ⇒ ∇ u ∈ B M O (R n) for the weak solutions of a class of quasilinear elliptic equations div a ∇ u ∇ u = div f in R n , where B (t) = ∫ 0 t τ a (τ) d τ for t ≥ 0. Meanwhile, we use the iteration-covering procedure to prove that B f ∈ L q (R n) ⇒ B ∇ u ∈ L q (R n) for any q > 1 for the weak solutions of div a ∇ u ∇ u = div a f f in R n. Moreover, we remark that a (t) = t p − 2 (p -Laplace equation) and a (t) = t p − 2 log (1 + t) satisfy the given conditions in this work. [ABSTRACT FROM AUTHOR]