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Displaying 41 – 60 of 96

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Piotr Hajłasz, Jacob Mirra (2013)

Analysis and Geometry in Metric Spaces

In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.

The martingale problem for a class of pseudo differential operators.

Walter Hoh (1994)

Mathematische Annalen

The mixed problem for a degenerate operator equation.

Tepoyan, Liparit (2008)

Bulletin of TICMI

The multiplication functions of Kučera

Kelly McKennon (1979)

Czechoslovak Mathematical Journal

The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues

Marita Gazzini, Enrico Serra (2008)

Annales de l'I.H.P. Analyse non linéaire

The non-archimedean Corona problem

Marius van der Put (1974)

Mémoires de la Société Mathématique de France

The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains.

Loredana Lanzani, Osvaldo Méndez (2006)

Revista Matemática Iberoamericana

The Properties of the Weighted Space $H_{2, α}^{k} (Ω)$ and Weighted Set $W_{2, α}^{k} (Ω, δ)$

V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)

Communications in Mathematics

We study the properties of the weighted space $H_{2, α}^{k} (Ω)$ and weighted set $W_{2, α}^{k} (Ω, δ)$ for boundary value problem with singularity.

The regularity of the positive part of functions in $L^{2} (I; H^{1} (Ω)) \cap H^{1} (I; H^{1} {(Ω)}^{*})$ with applications to parabolic equations

Daniel Wachsmuth (2016)

Commentationes Mathematicae Universitatis Carolinae

Let $u \in L^{2} (I; H^{1} (Ω))$ with $\partial_{t} u \in L^{2} (I; H^{1} {(Ω)}^{*})$ be given. Then we show by means of a counter-example that the positive part $u^{+}$ of $u$ has less regularity, in particular it holds $\partial_{t} u^{+} \notin L^{1} (I; H^{1} {(Ω)}^{*})$ in general. Nevertheless, $u^{+}$ satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.

The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions

Jean Dolbeault, Maria J. Esteban, Gabriella Tarantello (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We first discuss a class of inequalities of Onofri type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than $- 1$ . Without symmetry assumption, it holds if and only if the parameter is in the interval $(- 1, 0]$ . The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Caffarelli-Kohn-Nirenberg inequality, in two space dimensions. In fact, for suitable sets of parameters (asymptotically...

The sharp Sobolev inequality in quantitative form

Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)

Journal of the European Mathematical Society

The singular set of the minima of certain quadratic functionals

Mariano Giaquinta, Enrico Giusti (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Sobolev capacity on metric spaces.

Kinnunen, Juha, Martio, Olli (1996)

Annales Academiae Scientiarum Fennicae. Mathematica

The Sobolev embeddings are usually sharp.

Fraysse, A., Jaffard, S. (2005)

Abstract and Applied Analysis

The Sobolev spaces of harmonic functions

Ewa Ligocka (1986)

Studia Mathematica

The Sobolev-Besov imbedding theorem from the viewpoint of semi-groups of operators

H. Komatsu (1972/1973)

Séminaire Équations aux dérivées partielles (Polytechnique)

The Sobolev-Il'in theorem for the $B$ -Riesz potential.

Guliev, V.S., Garakhanova, N.N. (2009)

Sibirskij Matematicheskij Zhurnal

The trace of Sobolev and Besov spaces if 0 < p < 1

Björn Jaweth (1978)

Studia Mathematica

The Trace of Sobolev-Slobodeckij spaces on Lipschitz domains.

Jürgen Marschall (1987)

Manuscripta mathematica

The trace theorem $W_{p}^{2, 1} (Ω_{T}) ∋ f \mapsto \nabla_{x} f \in W_{p}^{1 - 1 / p, 1 / 2 - 1 / 2 p} (\partial Ω_{T})$ revisited

Peter Weidemaier (1991)

Commentationes Mathematicae Universitatis Carolinae

Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for $T ↓ 0$ . The proof is based on a version of Hardy’s inequality (cp. Appendix).

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