{'fraction_non_alphanumeric': 0.017429193899782137, 'fraction_numerical': 0.004357298474945534, 'mean_word_length': 4.609756097560975, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, '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}}
The Third Problem for the Laplace Equation on a Planar Cracked Domain with Modified Jump Conditions on Cracks

The paper studies the third problem for the Laplace equation on a cracked bounded planar domain with multiply connected Lipschitz boundary and boundary conditions from Lp. It is shown that, for 1 < p ≤ 2, there is a unique solution of the problem. This solution is constructed for a domain, which boundary is formed by curves with bounded rotation.