# Boundary Value Problems

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*f*belongs to a homogeneous Herz space K˙q(⋅)α,p(⋅) $\dot{K}^{\alpha,p(\cdot)}_{q(\cdot)}$ with two variable exponents.

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*k*Raviart–Thomas mixed elements and control is discretized by piecewise polynomials of degree

*k*. We adopt the mixed elliptic reconstruction to derive the a posteriori error estimates for...

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*f*is a continuous function with polynomial growth of order less than or equal...

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*p*-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)|u|p−2u=λf(x,u)in RN, $$ \Delta _{p}^{2} u+M \biggl( \int _{\mathbb{R}^{N}}\varPhi _{0}(x,\nabla u) \,dx \biggr) \operatorname{div}\bigl(\varphi (x,\nabla u)\bigr)+V(x) \vert u \vert ^{p-2}u=\lambda f(x,u) \quad \text{in } \mathbb{R}^{N}, $$ where 2<2p<N $2< 2p<N$, Δp2u=Δ(|Δu|p−2Δu) $\Delta...

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