ABSTRACT
In this chapter, we extend the results of Chapter 11 to the case when the Dirichlet boundary conditions are replaced with more general first-order boundary conditions. More precisely, we consider the operator ( A , D ( A ) ) = Tr ( Q ∇ ) + 〈 b , ∇ 〉 + c https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math12_3.tif"/> , assuming that 〈 Q ( x ) ξ , ξ 〉 ≥ μ | ξ | 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math12_4.tif"/> for every x ∈ ℝ d + https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math12_5.tif"/> , ξ ∈ ℝ d https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math12_6.tif"/> and some positive constant μ, and the boundary value problem λ u − ℝ d u = f , in ℝ d + , B u = g , on ∂ ℝ d + , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429262593/03624a6d-a4e5-45fb-ba52-c2b8f08b80c3/content/math12_7.tif"/>
