Elliptic equations with BMO nonlinearity in Reifenberg domains

Global Gradient Estimates for Nonlinear Elliptic Equations

“…We remark that the present result is a natural extension of previous research [9,20]. In fact, the problem (1.1) under the same conditions is considered in unweighted [9] and weighted [20] Lebesgue spaces.…”

“…In fact, the problem (1.1) under the same conditions is considered in unweighted [9] and weighted [20] Lebesgue spaces.…”

“…The existence and uniqueness of a weak solution to problem (1.1) can be obtained by the Minty-Browder method for monotone operators, see [9,20], under the assumption F ∈ L 2 (Ω, R n ), with the estimate…”

Nonlinear Muckenhoupt–Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations

“…We remark that the (δ, R 0 )-BMO condition allows A(x, ξ) has discontinuity in x and it can be used as an appropriate substitute for the Sarason [33] VMO condition (see, e.g., [5,6,18,25,34,37]). …”

“…In the case p = 2, the above (δ, R 0 )-BMO condition was introduced in [6], whereas such a condition for general p ∈ (1, ∞) appears in the recent paper [29]. We remark that the (δ, R 0 )-BMO condition allows A(x, ξ) has discontinuity in x and it can be used as an appropriate substitute for the Sarason [33] VMO condition (see, e.g., [5,6,18,25,34,37]).…”