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Entropy solutions for nonhomogeneous anisotropic \(\varDelta _{\vec{p}(\cdot)}\) problems. (English) Zbl 1316.35107

Authors’ abstract: We study a class of anisotropic nonlinear equations with variable exponent \(\vec{p}(\cdot )\) growth. We obtain the existence of entropy solutions by using the truncation technique and some a priori estimates.

MSC:

35J25 Boundary value problems for second-order elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J62 Quasilinear elliptic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B45 A priori estimates in context of PDEs
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