The Maximum Principle

By Patrizia Pucci, J. Serrin. 2007

221 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/17e09102ac06348b0912b4f7553ad73ae0f07b55

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Citations in the corpus

• Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “±∞. Due to the lack of regularity for problems (1.1), several tools, which are usually applied in the theory of multiplicity results based on the regularity results of Lieberman [21] and Pucci-Serrin [38], cannot be used in our treatment. Instead we will make use of the so-called Nehari manifold whi”
• Nonlinear nonhomogeneous singular problems (2019, unknown): “Hypotheses H(a)(i), (ii), (iii) are dictated by the nonlinear regularity theory of Lieberman [22] and the nonlinear maximum principle of Pucci and Serrin [40].”
• Geometry and Topology of some overdetermined elliptic problems (2012, methodology): “here f is a C1 function and α is a constant, see [27]. Moreover, the proof of J. Serrin can be generalized in order to obtain the same result when f is supposed to have only Lipschitz regularity, see [23], p. 196. The paper of Serrin was very important because it made the moving plane method availab”
• Moser iteration applied to elliptic equations with critical growth on the boundary (2018, methodology): “l y ∈ RN. 14 G.MARINO AND P.WINKERT Remark 3.4. We chose the special structure in H(A) to apply the nonlinear regularity theory, which is mainly based on the results of Lieberman [11] and PucciSerrin [15]. Closely related to this subject is also the work by Motreanu-MotreanuPapageorgiou [12]. If we ”
• BIFURCATING EXTREMAL DOMAINS FOR THE FIRST EIGENVALUE OF THE LAPLACIAN (2011, background): “Serrin’s result mentioned above continues to hold true for the overdetermined system (4): The only bounded domains where one can find a positive solution to (4) are round balls (see [23] for f ∈ C(1) and [20] for f Lipschitz).”
• Flattening Results for Elliptic PDEs in Unbounded Domains with Applications to Overdetermined Problems (2010, background): “1 on page 120 of [16]) give that”