We give, first, two new applications related to the range characterization of the range of trace operator in . After this, we characterize the range of trace operator in the Sobolev spaces when is a connected bounded domain with Lipschitz-continuous boundary.
On donne, d’abord, deux nouvelles applications relatives à la caractérisation de l’image de l’opérateur trace dans . Après cela, on caractérise l’image de l’opérateur trace dans les espaces de Sobolev , étant un domaine borné, connexe de de frontière lipschitzienne.
Accepted:
Published online:
Aissa Aibèche 1; Cherif Amrouche 2; Bassem Bahouli 2, 3
@article{CRMATH_2023__361_G3_587_0, author = {Aissa Aib\`eche and Cherif Amrouche and Bassem Bahouli}, title = {Trace {Operator{\textquoteright}s} {Range} {Characterization} for {Sobolev} {Spaces} on {Lipschitz} {Domains} of $\protect \mathbb{R}^2$}, journal = {Comptes Rendus. Math\'ematique}, pages = {587--597}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.407}, language = {en}, }
TY - JOUR AU - Aissa Aibèche AU - Cherif Amrouche AU - Bassem Bahouli TI - Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$ JO - Comptes Rendus. Mathématique PY - 2023 SP - 587 EP - 597 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.407 LA - en ID - CRMATH_2023__361_G3_587_0 ER -
%0 Journal Article %A Aissa Aibèche %A Cherif Amrouche %A Bassem Bahouli %T Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$ %J Comptes Rendus. Mathématique %D 2023 %P 587-597 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.407 %G en %F CRMATH_2023__361_G3_587_0
Aissa Aibèche; Cherif Amrouche; Bassem Bahouli. Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 587-597. doi : 10.5802/crmath.407. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.407/
[1] On the characterizations of matrix fields as linearized strain tensor fields, J. Math. Pures Appl., Volume 86 (2006) no. 2, pp. 116-132 | DOI | MR | Zbl
[2] Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czech. Math. J., Volume 44 (1994) no. 1, pp. 109-140 | DOI | MR | Zbl
[3] -theory for vector potentials and Sobolev’s inequalities for vector fields: Application to the Stokes equations with pressure boundary conditions, Math. Models Methods Appl. Sci., Volume 23 (2013) no. 1, pp. 37-92 | DOI | MR | Zbl
[4] On traces for for Lipschitz domains, J. Math. Anal. Appl., Volume 276 (2002) no. 2, pp. 845-867 | DOI | MR | Zbl
[5] On traces for in Lipschitz domains, C. R. Acad. Sci. Paris Sér. I Math., Volume 332 (2001) no. 8, pp. 699-704 | DOI | MR | Zbl
[6] On a vector version of a fundamental lemma of J. L. Lions, Chin. Ann. Math., Ser. B, Volume 39 (2018) no. 1, pp. 33-46 | DOI | MR | Zbl
[7] The Dirichlet problem for the biharmonic equation in Lipschitz domain, Ann. Inst. Fourier, Volume 36 (1986) no. 3, pp. 109-135 | DOI | Numdam | MR | Zbl
[8] On the traces of for a Lipschitz domain, Rev. Mat. Complut., Volume 14 (2001) no. 2, pp. 371-377 | MR | Zbl
[9] Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni ni n variabili, Rend. Semin. Mat. Univ. Padova, Volume 27 (1957), pp. 284-305 | Zbl
[10] Trace theorems for Sobolev spaces on Lipschitz domains. Necessary conditions, Ann. Math. Blaise Pascal, Volume 14 (2007) no. 2, pp. 187-197 | DOI | Numdam | MR | Zbl
[11] On the existence of the Airy function in Lipschitz domains. Application to the traces of , C. R. Acad. Sci. Paris Sér. I Math., Volume 330 (2000) no. 5, pp. 355-360 | DOI | MR | Zbl
[12] Elliptic Problems in Nonsmooth Domains, Monographs and Studies in Mathematics, 24, Pitman Advanced Publishing Program, 1985 | Zbl
[13] The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients, J. Anal. Math., Volume 110 (2010), pp. 167-239 | DOI | MR | Zbl
[14] Duality characterization of strain tensor distributions in arbitrary open set, J. Math. Anal. Appl., Volume 72 (1979), pp. 760-770 | DOI | MR | Zbl
[15] Équations aux dérivées partielles, Séminaire de Mathématiques Supérieures, 19, Presses de l’Université de Montréal, 1966 | Zbl
Cited by Sources:
Comments - Policy