POITWISE ESTIMATES OF WEAK SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS OF A DIVERGENCE TYPE WITH NONSTANDARD GROWTH CONDITIONS AND LOWER TERMS

С. Т. Акопян, Ю. С. Кудрич

Abstract


In the present work we obtain the pointwise estimates of the weak solutions to inhomogeneous quasilinear elliptic equations of the divergence type and lower terms. Our result generalizes the classical one obtained by T. Kilpelainen and J. Maly. With the help of nonlinear Wolff potential they proved the pointwise estimates of solutions to a quasilinear elliptic equation with the p-Laplace and measure µ on the right-hand side. Further, these estimates were generalized to strongly nonlinear equations and to strongly nonlinear subelliptic quasilinear equations and were applied as an efficient tool to the study of the questions of solvability and solutions regularity to various linear, quasilinear and nonlinear equations (see the works of J. Maly and W. Ziemer, G. Mingione and I.I. Skrypnik ). Due to application of some quasilinear equations with nonstandard growth conditions for the modeling of a behavior of electrorheological fluids, the qualitative theory of such equations is permanently developed, attracting the interest of researchers.


Keywords


quasilinear elliptic equations; Harnack inequality; poitwise estimates; weak solution; Wolff potentials

References


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