2020/02/22 by C. Fresneda-Portillo, Carlos Fresneda‐Portillo, Z. W. Woldemicheal +1 · 8 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary value problem #Differential Equations and Boundary Problems #Dirichlet integral #Dirichlet problem #Domain (mathematical analysis) #Equivalence (formal languages) #Lipschitz continuity #Lipschitz domain #Numerical methods in engineering #Partial differential equation #Sobolev space #Uniqueness #math.AP #math.FA #msc:31B10 #msc:35J25 #msc:45A05 #msc:45K05
paper · pdf · doi:10.1002/mma.6659
published in Mathematical Methods in the Applied Sciences 44(12), 9817-9830 (Wiley)
arxiv created 2020/02/22 · openalex created_date 2020/03/06 · openalex publication_date 2020/07/22 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/05
The interior Dirichlet boundary value problem for the diffusion equation in nonhomogeneous media is reduced to a system of boundary‐domain integral equations (BDIEs) employing the parametrix obtained in Portillo (2019). We further extend the results obtained in Portillo (2019) for the mixed problem in a smooth domain with L 2 (Ω) right‐hand side to Lipschitz domains and partial differential equation (PDE) right‐hand side in the Sobolev space H −1 (Ω), where neither the classical nor the canonical conormal derivatives are well‐defined. Equivalence between the system of BDIEs and the original BVP is proved along with their solvability and solution uniqueness in appropriate Sobolev spaces.