Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.

中文翻译：

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存在磁性台阶时超导性的破坏

许多早期的工作致力于研究 II 型超导有界平面域中的超导性击穿，并提交给平滑磁场。在目前的贡献中，我们考虑了一种新情况，其中施加的磁场是分段恒定的，并且不连续性跳跃沿着横向与边界相交的平滑曲线发生。为了处理这种情况，我们对一个新的有效模型进行了详细的光谱分析。因此，我们建立了从超导到正常状态的转变的单调性。此外，我们在样品完全消失之前确定了样品中超导性的位置。有趣的是，该研究显示了与受恒定场影响的角域情况的相似之处。