\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains

  • * Corresponding author: Paola Vernole

    * Corresponding author: Paola Vernole
Abstract Full Text(HTML) Figure(1) Related Papers Cited by
  • We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.

    Mathematics Subject Classification: Primary: 35J25, 35B65; Secondary: 35R02, 35B45.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  A possible example of domain $\Omega$. In this case $N=9$ and $\alpha=\alpha_7$

  • [1] D. E. Apushkinskaya and A. I. Nazarov, A survey of results on nonlinear Venttsel' problems, Application of Mathematics, 45 (2000), 69-80.  doi: 10.1023/A:1022288717033.
    [2] D. E. Apushkinskaya and A. I. Nazarov, Linear two-phase Venttsel' problems, Ark. Mat., 39 (2001), 201-222.  doi: 10.1007/BF02384554.
    [3] W. ArendtG. MetafuneD. Pallara and S. Romanelli, The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions, Semigroup Forum, 67 (2003), 247-261.  doi: 10.1007/s00233-002-0010-8.
    [4] F. Brezzi and G. Gilardi, Fundamentals of P. D. E. for Numerical Analysis, in: Finite Element Handbook (ed.: H. Kardestuncer and D. H. Norrie), McGraw-Hill Book Co., New York, 1987.
    [5] M. CefaloG. Dell'Acqua and M. R. Lancia, Numerical approximation of transmission problems across Koch-type highly conductive layers, Applied Mathematics and Computation, 218 (2012), 5453-5473.  doi: 10.1016/j.amc.2011.11.033.
    [6] M. CefaloM. R. Lancia and H. Liang, Heat flow problems across fractal mixtures: Regularity results of the solutions and numerical approximation, Differ. Integral Equ., 26 (2013), 1027-1054. 
    [7] G. Goldstein Ruiz, Derivation and physical interpretation of general boundary conditions, Adv. Differential Equations, 11 (2006), 457-480. 
    [8] G. Hardy, J. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.
    [9] V. A. Kondrat'ev,, Boundary-value problems for elliptic equations in domains with conical or angular point, Trans. Moscow Math. Soc., 16 (1967), 209-292. 
    [10] M. R. Lancia, Asymptotics for Venttsel' problems for operators in non divergence form in irregular domains, Discrete Contin. Dyn. Syst. Ser. S, 9 (2016), 1493-1520.  doi: 10.3934/dcdss.2016060.
    [11] M. R. LanciaA. Vélez-Santiago and P. Vernole, Quasi{linear Venttsel' problems with nonlocal boundary conditions, Nonlinear Anal. Real World Appl., 35 (2017), 265-291.  doi: 10.1016/j.nonrwa.2016.11.002.
    [12] M. R. Lancia and P. Vernole, Venttsel' problems in fractal domains, J. Evol. Equ., 14 (2014), 681-712.  doi: 10.1007/s00028-014-0233-7.
    [13] V. G. Maz'ya, Sobolev Spaces with Applications to Elliptic Partial Differential Equations, Springer-Verlag, 2011. doi: 10. 1007/978-3-642-15564-2.
    [14] A. I. Nazarov, On the nonstationary two-phase Venttsel problem in the transversal case, Problems in Mathematical Analysis, J. Math. Sci. (N. Y.), 122 (2004), 3251-3264.  doi: 10.1023/B:JOTH.0000031019.56619.4d.
    [15] S. A. Nazarov, B. A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries, de Gruyter, Berlin-New York, 1994. doi: 10. 1515/9783110848915. 525.
    [16] J. Necas, Les Mèthodes Directes en Thèorie des Èquationes Elliptiques, Masson, Paris, 1967.
    [17] A. Vélez-Santiago, Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions, J. Functional Analysis, 266 (2014), 560-615.  doi: 10.1016/j.jfa.2013.10.017.
    [18] A. Vélez-Santiago, Global regularity for a class of quasi{linear local and nonlocal elliptic equations on extension domains, J. Functional Analysis, 269 (2015), 1-46.  doi: 10.1016/j.jfa.2015.04.016.
    [19] A. D. Venttsel', On boundary conditions for multidimensional diffusion processes, Teor. Veroyatnost. i Primenen, 4 (1959), 172-185; English translation: Theor. Probability Appl., 4 (1959), 164-177.
    [20] M. Warma, An ultracontractivity property for semigroups generated by the p-Laplacian with nonlinear Wentzell-Robin boundary conditions, Adv. Differential Equations, 14 (2009), 771-800. 
    [21] M. Warma, The p-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets, Ann. Mat. Pura Appl., 193 (2014), 203-235.  doi: 10.1007/s10231-012-0273-y.
  • 加载中

Figures(1)

SHARE

Article Metrics

HTML views(223) PDF downloads(218) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return