Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 4

Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth

Sayfa
1383–1396
Yayın Tarihi
2022-10-18
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)

Finally, we present an application for defined spaces to the stochastic partial differential equations with stochastic field growth.*********************************************************************************************************************************************************************

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta }^{k,p(.,.)}\left( D\times \Omega \right) $.
📊
Temel Bulgular & Veri:Also, we study some basic properties and embeddings of these spaces.
💡
Sonuç & Katkı:Finally, we present an application for defined spaces to the stochastic partial differential equations with stochastic field growth.*********************************************************************************************************************************************************************
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Quasilinear elliptic equation · Weighted stochastic field exponent Sobolev spaces · Pseudo-monotone operator

Abstract

In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta }^{k,p(.,.)}\left( D\times \Omega \right) $. Also, we study some basic properties and embeddings of these spaces. Finally, we present an application for defined spaces to the stochastic partial differential equations with stochastic field growth.*********************************************************************************************************************************************************************

🔖

Bu Makaleye Atıf Yap

Ünal, C., Aydın, İ. (2022). Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1383–1396. https://ajindex.com/articles/530043

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. H. Aoyama, Lebesgue spaces with variable on a probability space, Hiroshima Math. J. 39, 207–216, 2009
  2. F.E. Browder, Pseudo-monotone operators and nonlinear elliptic boundary value problems on unbounded domains, Proc. Natl. Acad. Sci. USA, 74 (7), 2659–2661, 1977
  3. H. Cartan, Differential Calculus, Herman, Paris-France, 1971
  4. B. Cekic, R. Mashiyev and G.T. Alisoy, On the Sobolev-type inequality for Lebesgue spaces with a variable exponent, Int. Math. Forum, 1 (27), 1313–1323, 2006
  5. L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin, 2011
  6. X.L. Fan, Solutions for $p\left( x\right) $-Laplacian Dirichlet problems with singular coefficients, J. Math. Anal. Appl. 312, 464–477, 2005
  7. P. Harjulehto, P. Hästö, M. Koskenoja and S. Varonen, The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal. 25, 205–222, 2006
  8. P. Harjulehto, P. Hästö, U.V. Le and M. Nuortio, Overview of differential equations with non-standard growth, Nonlinear Anal. 72, 4551–4574, 2010
  9. O. Kováčik and J. Rákosník, On spaces $L^{p(x)}$ and $W^{k,p(x)}$, Czechoslovak Math. J. 41(116) (4), 592–618, 1991
  10. B. Lahmi, E. Azroul and K. El Haitin, Nonlinear degenerated elliptic problems with dual data and nonstandard growth, Math. Reports 20(70) (1), 81–91, 2018
  11. R.A. Mashiyev, S. Oğraş, Z. Yucedag and M. Avci, The Nehari manifold approach for Dirichlet problem involving the $p\left(x\right) $-Laplacian equation, J. Korean Math. Soc. 47 (4), 845–860, 2010
  12. M. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations (Second Edition), Springer, 2004
  13. M. Růžička, Electrorheological fluids: modeling and mathematical theory, Springer, Berlin Heidelberg New York, 2000
  14. B. Tian, Y. Fu and B. Xu, Function spaces with a random variable exponent, Abstr. Appl. Anal. 2011, Article ID 179068, 2011
  15. B. Tian, B. Xu and Y. Fu, Stochastic field exponent function spaces with applications, Complex Var. Elliptic Equ. 59 (1), 133–148, 2014
  16. C. Unal and I. Aydın, Weighted variable exponent Sobolev spaces with zero boundary values and capacity estimates, Sigma J. Eng. & Nat. Sci. 36 (2), 371–386, 2018.