We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include...We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.展开更多
We describe an application of the partial differential inclusion method to the existence of Lipschitz weak solutions for certain forward-backward diffusion equations including the one-dimensional version of the Perona...We describe an application of the partial differential inclusion method to the existence of Lipschitz weak solutions for certain forward-backward diffusion equations including the one-dimensional version of the Perona-Malik equation in image processing.展开更多
文摘We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.
文摘We describe an application of the partial differential inclusion method to the existence of Lipschitz weak solutions for certain forward-backward diffusion equations including the one-dimensional version of the Perona-Malik equation in image processing.
