{'fraction_non_alphanumeric': 0.03067484662576687, 'fraction_numerical': 0.007361963190184049, 'mean_word_length': 4.037037037037037, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the structure of level sets and the growth of subsolutions of equations of elliptic type

In [1] Landis established a relation between the number of connected components of a level set of a solution of a linear equation of elliptic type and the rate of growth of the solution. This note is devoted to the examination of the more general case in which the number of connected components is infinite, generally speaking; here we establish a relation between the rate of growth and the disposition of the components with respect to one another. The author is grateful to E.M. Landis for consultations and to B.V. Shabat for a discussion of the subject of this paper. 1. Let aj(x, £) (/ = 1 or 2) be measurable functions defined for almost all χ e R and £ e R. Suppose that there are constants ν γ, ι>2 > 0 such that