Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 4, 1383 - 1396, 06.08.2020
https://doi.org/10.15672/hujms.561682

Öz

Kaynakça

  • [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.

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

Yıl 2020, Cilt: 49 Sayı: 4, 1383 - 1396, 06.08.2020
https://doi.org/10.15672/hujms.561682

Öz

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.

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Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

İsmail Aydın 0000-0001-8371-3185

Cihan Unal 0000-0002-7242-393X

Yayımlanma Tarihi 6 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 4

Kaynak Göster

APA Aydın, İ., & Unal, C. (2020). Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics, 49(4), 1383-1396. https://doi.org/10.15672/hujms.561682
AMA Aydın İ, Unal C. Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics. Ağustos 2020;49(4):1383-1396. doi:10.15672/hujms.561682
Chicago Aydın, İsmail, ve Cihan Unal. “Weighted Stochastic Field Exponent Sobolev Spaces and Nonlinear Degenerated Elliptic Problem With Nonstandard Growth”. Hacettepe Journal of Mathematics and Statistics 49, sy. 4 (Ağustos 2020): 1383-96. https://doi.org/10.15672/hujms.561682.
EndNote Aydın İ, Unal C (01 Ağustos 2020) Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics 49 4 1383–1396.
IEEE İ. Aydın ve C. Unal, “Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, ss. 1383–1396, 2020, doi: 10.15672/hujms.561682.
ISNAD Aydın, İsmail - Unal, Cihan. “Weighted Stochastic Field Exponent Sobolev Spaces and Nonlinear Degenerated Elliptic Problem With Nonstandard Growth”. Hacettepe Journal of Mathematics and Statistics 49/4 (Ağustos 2020), 1383-1396. https://doi.org/10.15672/hujms.561682.
JAMA Aydın İ, Unal C. Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics. 2020;49:1383–1396.
MLA Aydın, İsmail ve Cihan Unal. “Weighted Stochastic Field Exponent Sobolev Spaces and Nonlinear Degenerated Elliptic Problem With Nonstandard Growth”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, 2020, ss. 1383-96, doi:10.15672/hujms.561682.
Vancouver Aydın İ, Unal C. Weighted stochastic field exponent Sobolev spaces and nonlinear degenerated elliptic problem with nonstandard growth. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1383-96.