Решения дифференциального неравенства с нуль-лагранжианом: повышающаяся интегрируемость и устранимость особенностей. I

Автор: Егоров Александр Анатольевич

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.16, 2014 года.

Бесплатный доступ

Целью настоящей статьи является установление свойства самоулучшающейся интегрируемости производных решений дифференциального неравенства с нуль-лагранжианом. Более точно, мы доказываем, что решение класса Соболева с показателем суммирумости, немного меньшим естественно определенного структурными предположениями на нуль-лагранжиан показателя, фактически принадлежит пространству Соболева с показателем суммируемости, немного большим естественного показателя. Мы также применяем это свойство, чтобы улучшить теоремы о гельдеровой регулярности и об устойчивости из статьи [19].

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