Extreme problems in minimax signal detection for $l_q$-ellipsoids with $l_p$-balls removed

Asymptotically minimax problem of signal detection is considered for signals from $l_q$-ellisoids with $l_p$-ball removed ($p>2$ or $p<2$, $q<p$) and Gaussian white noise. Assymptotically exact condition of distinguishability are obtained as well as estimates of minimax probability of errors for axes of ellipsoids $a_n\asymp n^{-\lambda}$, $\lambda>0$. Bibl. 6 titles.