KaydedilenlerDerginizi ekleyin

Dergiler / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2018 / Cilt: 36 - Sayı: 2

WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES WITH ZERO BOUNDARY VALUES AND CAPACITY ESTIMATES

Cihan ÜNAL
İsmail AYDIN
Sayfa
373–388
Yayın Tarihi
2018-06-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We will introduce a capacity in sense to this defined space and, also, give several estimates.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we define weighted variable exponent Sobolev space with zero boundary values and investigate some properties of this space with weighted variable Sobolev capacity.
📊
Temel Bulgular & Veri:We obtain Poincaré inequality with respect to zero boundary values.
💡
Sonuç & Katkı:We will introduce a capacity in sense to this defined space and, also, give several estimates.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Weighted variable exponent Sobolev spaces · Sobolev capacity · energy integral.

Abstract

In this paper, we define weighted variable exponent Sobolev space with zero boundary values and investigate some properties of this space with weighted variable Sobolev capacity. We obtain Poincaré inequality with respect to zero boundary values. We will introduce a capacity in sense to this defined space and, also, give several estimates.

🔖

Bu Makaleye Atıf Yap

ÜNAL, C., AYDIN, İ. (2018). WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES WITH ZERO BOUNDARY VALUES AND CAPACITY ESTIMATES. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 36 - Sayı: 2, 373–388. https://ajindex.com/articles/419174

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. Acerbi E., Mingione G., (2001) Regularity Results for a Class of Functionals with Non-Standard Growth, Arch. Ration. Mech. and Anal., Vol. 156, 121-140
  2. Aydın I., (2012) On Variable Exponent Amalgam Spaces, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat., Vol. XX, Fasc. 3
  3. Aydın I., (2012) Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and Applications, Vol. 2012, Article ID 132690, 17 pages, doi:10.1155/2012/132690
  4. Baroni P., Habermann J., (2014) Elliptic Interpolation Estimates for Non-Standard Growth Operators, Ann. Acad. Sci. Fenn. Math., Vol. 39, 119-162
  5. Bui T. A., Duong X. T., (2017) Weighted Variable Exponent Sobolev Estimates for Elliptic Equations with Non-Standard Growth and Measure Data, (preprint),
  6. Coscia A., Mingione G., (1999) Hölder Continuity of the Gradient of - Harmonic Mappings, C. R. Acad. Sci. Paris, Ser. 1 Math., Vol. 328, No. 4, 363-368
  7. Diening L., (2004) Maximal Function on Generalized Lebesgue Spaces, Math. Inequal. Appl., Vol. 7, No. 2, 245-253
  8. Diening L., Hästö P. Muckenhoupt Weights in Variable Exponent Spaces, (preprint)
  9. Diening L., Hästö P., Nekvinda A., (2004) Open Problems in Variable Exponent Lebesgue and Sobolev Spaces, In Proceedings of the Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA' 04), Milovy, Czech, 38-58
  10. Diening L., Harjulehto P., Hästö P., Růžička M., (2011) Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin
  11. Dinca G., (2009) A fixed Point Method for the - Laplacian, C. R. Acad. Sci. Paris, Ser. I, Vol. 347, 757-762
  12. Evans L. C., Gariepy R.F., (1992) Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA
  13. Fan X., Zhao D., (2001) On the Spaces and, J. Math. Anal. Appl., Vol. 263, No. 2, 424-446
  14. Fan X., Zhang Q., (2003) Existence of Solutions for - Laplacian Dirichlet Problem, Nonlinear Anal., Vol. 52, 1843-1852
  15. Gilbarg D., Trudinger N. S., (1977) Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin
  16. Harjulehto P., Hästö P., Koskenoja M., (2007) Properties of Capacities in Variable Exponent Sobolev Spaces, Journal of Analysis and Applications, Vol. 5, No. 2, 71-92
  17. Harjulehto P., Hästö P., Koskenoja M., (2003) The Dirichlet Energy Integral on Intervals in Variable Exponent Sobolev Spaces, Z. Anal. Anwend., Vol. 22, No. 4, 911-923. [1