scholarly journals Elliptic problems with rough boundary data in generalized Sobolev spaces

2020 ◽  
Vol 0 (0) ◽  
pp. 1-39
Author(s):  
Anna Anop ◽  
◽  
Robert Denk ◽  
Aleksandr Murach ◽  
Keyword(s):  
Sobolev Spaces ◽  
Boundary Data ◽  
Elliptic Problems ◽  
Rough Boundary ◽  
Generalized Sobolev Spaces

scholarly journals Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

Embeddings of weighted Sobolev spaces and degenerate elliptic problems

2017 ◽  
Vol 60 (8) ◽  
pp. 1399-1418 ◽  
Author(s):  
ZongMing Guo ◽  
LinFeng Mei ◽  
FangShu Wan ◽  
XiaoHong Guan
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Elliptic Problems ◽  
Degenerate Elliptic

scholarly journals A strong maximum principle for the fractional laplace equation with mixed boundary condition

2021 ◽  
Vol 24 (6) ◽  
pp. 1699-1715
Author(s):  
Rafael López-Soriano ◽  
Alejandro Ortega
Keyword(s):  
Boundary Condition ◽  
Maximum Principle ◽  
Laplace Equation ◽  
Boundary Data ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Strong Maximum Principle ◽  
The One

Abstract In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet–Neumann boundary data which extends the one proved by J. Dávila (cf. [11]) to the fractional setting. In particular, we present a comparison result for two solutions of the fractional Laplace equation involving the spectral fractional Laplacian endowed with homogeneous mixed boundary condition. This result represents a non–local counterpart to a Hopf’s Lemma for fractional elliptic problems with mixed boundary data.

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