ON SOBOLEV-VISIK-DUBINSKII TYPE INEQUALITIES
Keywords:Sobolev-Visik-Dubinski1type inequalities, functions of several inde pendent variables, first order partial derivatives, Holder's inequality, arithmetic mean-·geometric mean inequality
In the present paper we establish some new integral inequalities of the Sobolev-Visik Dubinskii type involving functions of several independent variables and their first order partial derivatives. The analysis used in the proofs is elementary and the obtained results provide new estimates on these types of inequalities.
R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
R. P. Agarwal, J. Pecaric and I. Emetic, Improved integral inequalities in n independent variables, Computers Math. Applic., 33(1997), 27-38
H. Alzer, Some integral and discrete inequalities in several independent variables, Math Comput. Modelling, 25(1997), 97-104.
P. S. Bullen, D. S. Mitrinovic and P. M. Vasic, Means and Their Inequalities, Reidel, Dordrecht, 1988.
J. A. DubinskiI, Some integral inequalities and the solvability of degenerate quasilinear elliptic systems of differential equations, Math. Sb., 64(1964), 458-480.
C. 0 . Horgan and L. T. Wheeler, Spatial decay estimates for the Havier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math., 35(1978), 97-116
B. G. Pachpatte, On Sobolev type integral inequalities, Proc. Royal Soc. Edinburgh 103A(1986), 1-14
B. G. Pachpatte, On Poincare-type integral inequalities, J. Math. Anal. Appl., 114(1986), 111- 115.
B. G. Pachpatte, On two inequalities of the Serrin type, J. Math. Anal. Appl., 116(1986), 193-199.
B. G. Pachpatte, A note on two multidimensional integral inequalities, Utilitas Mathemetica, 30(1986), 123-129.
B. G. Pachpatte, A note on multidimensional integral inequalities, J. Math. Anal. Appl., 122(1987), 122-128.
B. G. Pachpatte, A note on Poincare and Sobolev type integral inequal中 es, Tamkang J Math., 18(1987), 1-7
B. G. Pachpatte, On Sobolev-Lieb-Thirring type inequalities, Chinese J. Math. 18(1990), 385-397.
B. G. Pachpatte, On some variants of Sobolev's inequality, Soochow J. Math., 17(1991), 121 - 129.
S. L. Sobolev, Some applications of functional analysis in mathematical physics, Izdat. Leningrad. Gos. Univ., Leningrad, 1950, English transl., Transl. Math. Monographs, Vol 7, Amer. Math. Soc., Providence, R. I. 1963.
M. I. Visik, On the solvab·iiity of the first boundary value problem for nonlinear elliptic systems of differential equations, Dokl. Akad. Nauk SSSR, 134(1960), 749-752 =Soviet Math. Dokl., 1(1960), 1126-1129.
How to Cite
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.