The Dirichlet problem for \(\alpha\)-harmonic functions on conical domains
From MaRDI portal
Publication:819615
DOI10.5802/ambp.208zbMath1100.31004OpenAlexW2332992786MaRDI QIDQ819615
Krzysztof Bogdan, Tomasz Jakubowski
Publication date: 29 March 2006
Published in: Annales Mathématiques Blaise Pascal (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AMBP_2005__12_2_297_0
Boundary value problems for second-order elliptic equations (35J25) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)
Related Items
Boundary behavior of \(\alpha \)-harmonic functions on the complement of the sphere and hyperplane ⋮ Self-similar solution for fractional Laplacian in cones ⋮ Kelvin transform for α-harmonic functions in regular domains ⋮ Yaglom limit for stable processes in cones ⋮ Hitting half-spaces by Bessel-Brownian diffusions ⋮ Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Lévy processes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Boundary Harnack Principle for fractional powers of Laplacian on the Sierpiński carpet
- Estimates of harmonic measure
- Estimates on Green functions and Poisson kernels for symmetric stable processes
- Probabilistic proof of boundary Harnack principle for \(\alpha\)-harmonic functions
- Relative Fatou theorem for \(\alpha\)-harmonic functions in Lipschitz domains
- Symmetric stable processes in cones
- Sharp estimates for the Green function in Lipschitz domains
- Sharp estimates of the Green function, the Poisson kernel and the Martin kernel of cones for symmetric stable processes
- An identity with applications to harmonic measure
- Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
- The boundary Harnack principle for the fractional Laplacian
