Integrability of very weak solution to the Dirichlet problem of nonlinear elliptic system
| dc.contributor.author | Tong, Yuxia | |
| dc.contributor.author | Liang, Shuang | |
| dc.contributor.author | Zheng, Shenzhou | |
| dc.date.accessioned | 2021-10-13T14:34:56Z | |
| dc.date.available | 2021-10-13T14:34:56Z | |
| dc.date.issued | 2019-01-02 | |
| dc.description.abstract | This article concerns the higher integrability of a very weak solution u ∈ θ + W1,r0(Ω) for max{1, p - 1} < r < p < n to the Dirichlet problem of the nonlinear elliptic system -DαAαi(x, Du) = Bi(x, Du) in Ω, u = θ on ∂Ω, where A(x, Du) = (Aαi(x, Du)) for α = 1,..., n and i = 1,..., m, and each entry of B(x, Du) = Bi(x, Du)) for i = 1,..., m satisfies the monotonicity and controllable growth. If θ ∈ W1,q(Ω) for q > r, then we derive that the very weak solution u of above-mentioned problem is integrable with u ∈ {θ + Lq*weak(Ω) for 1 ≤ q < n, θ + Lτ(Ω) for q = n and 1 < τ < ∞, θ + L∞(Ω) for q > n, provided that r is sufficiently close to p, where q* = qn/(n - q). | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 11 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Tong, Y., Liang, S., & Zheng, S. (2019). Integrability of very weak solution to the Dirichlet problem of nonlinear elliptic system. <i>Electronic Journal of Differential Equations, 2019</i>(01), pp. 1-11. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14644 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Integrability | |
| dc.subject | Very weak solution | |
| dc.subject | Nonlinear elliptic system | |
| dc.subject | Controllable growth | |
| dc.title | Integrability of very weak solution to the Dirichlet problem of nonlinear elliptic system | |
| dc.type | Article |