Harmonic functions satisfying weighted sign conditions on the boundary
Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces H... and N*.
Harmonic majorization of in subsets of , .
Harmonic mappings of surfaces
Harmonic mappings onto parallel slit domains
We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.
Harmonic measure of some Cantor type sets.
Harmonic measures for symmetric stable processes
Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and that determine whether ω(S,D) is zero or positive.
Harmonic measures of perforated domains
Harmonic morphisms and non-linear potential theory
Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e., a harmonic...
Harmonic morphisms and subharmonic functions.
Harmonic spaces associated with adjoints of linear elliptic operators
Let be an elliptic linear operator in a domain in . We imposse only weak regularity conditions on the coefficients. Then the adjoint exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type given distribution. We then apply to R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of are also studied. The results generalize earlier work of the author.
Harmonic Spaces Associated with Non-Symmetric Translation Invariant Dirichlet Forms.
Harmonic spaces associated with parabolic and elliptic differential operators.
Harmonic univalent functions defined by an integral operator.
Harmonické funkce a věty o průměru
Harmonie Continuation and Removable Singularities in the Axiomatic Potential Theory.
Harmonie Functions of Bounded Mean Oscillation.
Harmonische Formen in einer Matrixvariablen.
Harnack inequalities for Schrödinger operators
Harnack inequality for the Schrödinger problem relative to strongly local Riemannian -homogeneous forms with a potential in the Kato class.