Entropy solutions for nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity

Nonlinear Degenerate Anisotropic Elliptic Equations with Variable Exponents and L¹ Data

“…and f ∈ L m (Ω), with m ≥ 1, existence and regularity results of distributional solutions have been proved in [3]. As far as the existence results for our problem (1.1) there are three difficulties associated with this kind of problems.…”

“…Eq., 33 (2020), pp. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Carathéodory functions such that for almost every x in Ω and for every (σ,ξ) ∈ R×R N the following assumptions are satisfied for all i = 1,..., N…”

“…The operator A possesses more complicated nonlinearities; thus, some techniques used in the constant exponent case cannot be carried out for the variable exponent case. For more recent results for elliptic and parabolic case, see the papers [4][5][6][7][8] and references therein. The paper is organized as follows.…”

Bounded Solutions for Anisotropic Degenerate Parabolic Problems with Singular Term

“…θ = 0 and γ = 0), it is proved the existence results for the problems (1.1) in [19,20] when f ∈ L m (Q) or f is a bounded Radon measure on Q. If γ = 0, The existence and regularity of the entropy solutions for (1.1) with lower order terms and variable exponents were considered in [28]. The problem (1.7) was then generalized in [30], when the authors studied the following singular problem…”