A strong maximum principle for the fractional laplace equation with mixed boundary condition
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Rafael López-Soriano
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.
Acknowledgements
This work has been supported by the Madrid Government under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). The authors are partially supported by the Ministry of Economy and Competitiveness of Spain, under research project PID2019-106122GB-I00.
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© 2021 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–6–2021)
- Research Paper
- Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces
- B-spline collocation discretizations of caputo and Riemann-Liouville derivatives: A matrix comparison
- A strong maximum principle for the fractional laplace equation with mixed boundary condition
- Difference between Riesz derivative and fractional Laplacian on the proper subset of ℝ
- Some properties of the fractal convolution of functions
- Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations
- Discrete fractional boundary value problems and inequalities
- On the generalized fractional Laplacian
- Recent developments on the realization of fractance device
- Explicit representation of discrete fractional resolvent families in Banach spaces
- Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems
- Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
- An inverse problem approach to determine possible memory length of fractional differential equations
Artikel in diesem Heft
- Frontmatter
- Editorial
- FCAA related news, events and books (FCAA–volume 24–6–2021)
- Research Paper
- Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces
- B-spline collocation discretizations of caputo and Riemann-Liouville derivatives: A matrix comparison
- A strong maximum principle for the fractional laplace equation with mixed boundary condition
- Difference between Riesz derivative and fractional Laplacian on the proper subset of ℝ
- Some properties of the fractal convolution of functions
- Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations
- Discrete fractional boundary value problems and inequalities
- On the generalized fractional Laplacian
- Recent developments on the realization of fractance device
- Explicit representation of discrete fractional resolvent families in Banach spaces
- Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems
- Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
- An inverse problem approach to determine possible memory length of fractional differential equations
